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Solar  and  Planetary 
Physics  and  Motion 


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COPYRIGHTED.  NOVEMBER.  1907 
By  the  Author 

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Solar  and  Planetary 
Physics  and  Motion 


COPYRIGHTED.  NOVEMBER.  1907 
By  the  Author 

EDWARD  LYNCH 


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>^ 


"  To  the  Stars  Through  Difficulties  " 

In  ^TliCemoTy)  of 

jr.  3ot?n  H.  ^rggorg 

First  President  of 

(lli|g  MmpprgUii  of  dlUtmita 

These  pages  are  Dedicated 


.<-t*-^^»  *'"»*-»  • 


PREFACE. 

The  economic  value  of  a  sure  basis  of  prediction  in  meteorology  is  inesti- 
mable. The  value  to  the  nation  of  a  reliable  forecast  of  the  season,  of 
probable  rain  supply,  of  drouths,  of  extraordinary  degrees  of  heat  or  cold, 
weeks  or  even  months  in  advance  of  the  events,  cannot  be  estimated  in 
money.  Weather  bureau  experts  and  other  scientific  men  have  labored  long 
in  search  for  a  periodic  law  of  recurrence  of  weather  conditions.  Publica- 
tions by  thousands  have  been  issued  tabulating  results  of  careful  research 
into  past  weather  conditions. 

The  sun  and  its  constitution  is  the  final  physical  cause  of  all  condition.^? 
which  make  life  sustainable  on  the  earth.  The  sun  has  been  subjected  to 
every  possible  form  of  scrutiny  in  the  endeavor  to  understand  the  laws  of 
its  being  and  the  causes  of  its  manifest  variability. 

This  is  another  attempt.  I  am  persuaded  that  the  tables  given  herein 
summarize  a  law  of  periodic  solar  action  which  will  render  prediction  of 
future  solar  action  precise  as  to  time  and  definite  as  to  intensity.  These 
tables  are  based  entirely  upon  rigorous  calculations  of  events  and  facts  open 
to  the  scrutiny  of  all.     Personal  bias  and  vanity  can  not  sway  the  results. 

If  the  writer  is  mistaken  in  this  statement  then  those  tables  present  the 
most  remarkable  combination  of  figures  and  fiction,  extending  over  300 
years,  to  be  found  in  the  history-  of  mathematics.  So  chameleon  like  are  the 
figured  results  of  planetary  action  that  they  simulate  the  precise  form  and 
physical  conditions,  as  to  time  and  intensity,  of  solar  storm  and  calm :  and 
they  seem  to  truthfully  reflect  every  well  estabKshed  rule  of  solar  action 
derived  from  observations  extending  over  300  years.  Spots  come  and  go  on 
the  sun  at  irregular  intervals ;  no  two  periods  of  maxima  or  minima  occur  of 
equal  length  in  succession  nor  indeed  at  alL  Yet  these  tables,  derived 
n}(r(ly  from  ihf  motions  of  the  planets  and  the  sun,  follow  these  spot  condi- 
tions, through  all  their  sinuosities,  telling  of  the  waxing  and  waning  of  solar 
activity  as  if  they  were  derived  from  close  scrutiny  of  that  condition. 

Certainly,  therefore,  if  these  pages  do  not  teU  the  truth  they  are  most 
interesting  fiction,  and  are  illustrative  of  the  ability  of  plausible  figures 
to  lie. 

EDWARD  LYNTH. 
1330  Caeolixe  Street,  Alajjeda.  California,  October  8th,  1907. 


A    PRELIMINARY    CHAPTER    ON    SOLAR    PHYSICS. 

The  object  of  this  chapter  is  to  briefly  state  a  theory,  founded  upon  a 
broad  basis  of  fact,  of  the  causes  of  solar  activity ;  especially  dealing  with 
the  periodicity  of  sun-spots,  because  the  knowledge  of  the  periodical  varia- 
tion of  sun-spots  is  the  most  definite  and  extended,  covering  three  hundred 
years  of  the  sun 's  history. 

This  theory  rests  upon  a  new  and  more  extended  examination  of  the 
effects  of  gravitation  by  the  great  planets  upon  the  sun,  especially  upon  its 
movement  towards  its  apex. 

The  activity  of  the  sun  is  manifested  directlij  by  its  spot  periods,  its 
coronas,  and  its  variable  shape;  and,  indirectly,  by  terrestrial  phenomena 
which  happen  at  the  same  time  with  solar  disturbance,  namely,  periodical 
variation  in  magnetic  declination,  aurora  borealis,  extraordinary  heat, 
cold,  and  wind  and  electrical  storms.  In  addition  I  will  at  some  future 
time  publish  detailed  reasons  for  including  some  kinds  of  earthquakes  in 
this  list  of  effects  indirectly  manifested,  giving  merely  a  sketch  at  this  time. 
A  brief  summary  of  the  present  state  of  learning  as  to  the  causes  of  solar 
activity  and  the  present  theories,  based  upon  observation,  of  its  effects  is 
necessary  to  the  introduction  of  this  chapter. 

In  1903  Miss  Gierke  published  ''Problems  in  Astrophysics,"  in  which  she 
said : 

''The  sun  is  subject  to  a  rhythmical  tide  of  disturbance,  ebbing  and  flow- 
ing in  about  eleven  years.  But  the  flow  is  irregular  and  spasmodic.  Both 
the  intensity  of  the  crises  and  the  intervals  at  which  they  recur  vary  largely 
and  unaccountably.  Probably  the  eleven  year  cycle  is  involved  in  others. 
One,  there  is  reason  to  believe,  brings  about  alternate  accentuations  and  par- 
tial effacements  of  change  comprised  within  a  term  of  some  sixty-five  years. 
And  minor  pulsations — wavelets  on  the  great  rollers — are  besides  evident. 
Prediction  nevertheless  remains  at  fault.  Spot  maxima  are  delayed  or 
anticipated,  they  are  lanquid  or  energetic,  as  the  outcome  of  modes  of  action 
defying  calculation.  *  *  *  The  error  of  the  spot  period  may  amount  to 
nearly  half  its  normal  length.  Thus  sixteen  years  elapsed  between  the  max- 
imum of  1788  and  the  next  certainly  ensuing,  and  only  7.3  years  separated 
the  culminating  points  in  1829.9  and  1837.2     *     *     * 

' '  The  throbbings  of  solar  agitation  aft'ect  his  entire  system.  In  how  many 
ways,  and  by  what  hidden  means,  we  can  but  vaguely  surmise.  Terrestrial 
meteorology,  as  a  whole,  is  certainly  embraced  in  the  great  cycle,  although 
the  details  of  its  conformity  baffle  by  their  intricacy,  the  most  painstaking 
pursuit.     *     *     * 


"A  prolouc:ed  solar  calm  appears  to  have  set  in  about  164:3.  Galileo  and 
Seheiner  had  been  at  no  loss  for  subjects  of  study;  but  the  diligence  of  their 
successoi-s,  althouixh  unrelaxed,  went  mostly  unre(iuited.     *     *     * 

"Definitively  the  protracted  minimum  came  to  an  end  in  171G  and  therj 
was  a  normal  maximum  in  1718.     *     *     * 

"Indi^^dual  outbreaks  on  the  sun  are  often  unmistakably  associated  with 
commotions  of  the  magnetic  system.  These  so  called  'storms'  are  world 
wide  in  their  nature,  abrupt  in  their  origin,  and  bear  witness  to  some  vital 
spasm  attacking  the  globe  as  a  whole,  and  at  once.     *     *     * 

''Little  progress  has  been  made  towards  ascertaining  the  cause  of  solar 
periodicity.  We  are  only  assured  that  it  is  not  imposed  from  without,  but 
arises  from  within;  it  resembles  a  'free'  rather  than  a  'forced  vibration.' 
This  conclusion,  it  is  true,  tends  to  relegate  the  matter  to  obscurity  for  the 
interior  of  the  sun  is  terra  incognita  and  seems  likely  to  remain  so.  His 
cyclical  changes  may  belong  to  his  original  constitution  ;  they  maj'  date  from 
nebular  times,  and  be  as  inherent  as  the  tone  of  a  bell.  Or  they  may  simply 
characterize  a  change  of  growth,  and  prove  liable  to  modification  and  efface- 
ment."     (pp.  151-160.) 

In  another  of  her  works  ]\Iiss  Gierke  says : 

"The  idea  that  solar  maculation  depends  in  some  way  upon  the  position 
of  the  planets  occurred  to  Galileo  in  1612  (citing  Opere,  t.  iii,  p.  412).  It 
has  been  industriously  sifted  by  a  whole  bevy  of  modern  solar  physicists. 
V'  Wolf  in  1859  found  reason  to  believe  that  the  eleven  year  curve  is  deter- 
mined by  the  action  of  Jupiter,  modified  by  that  of  Saturn,  and  diversified 
by  influences  proceeding  from  the  earth  and  Venus.  '  Its  tempting  approach 
to  agreement  with  Jupiter's  period  of  revolution  round  the  sun,  indeed, 
irresistibly  suggested  a  causal  connection;  yet  it  does  not  seem  that  the 
most  skilful  'coaxing'  of  figures  can  bring  about  a  fundamental  harmony. 
Carrington  pointed  out  in  1863,  that  while,  during  eight  successive  periods, 
from  1770  downwards,  there  were  approximate  coincidences  between  Jupi- 
ter's aphelion  pasages  and  sun-spot  maxima,  the  relation  had  been  almost 
exactly  reversed  in  the  two  periods  preceding  that  date  "(citing  Observa- 
tions at  Redhill,  p.  248)  ;  "and  the  latest  conclusion  of  ^I.  Wolf  himself  is 
that  the  Jovian  origin  must  be  abandoned."  (Citing  Compte's  Rendus, 
t.  xcv,  p.  1249.) 

"M.  Duponchel  of  Paris  was  nevertheless  not  wholly  unsuccessful  in 
accommodating  discrepancies  with  the  help  of  perturbations  by  the  large 
exterior  planets;  since  his  prediction  of  an  abnoi-mal  lengthening  of  the 
maximum  of  1883-4  through  certain  peculiarities  in  the  position  of  Uranus 
and  Neptune  about  the  time  it  fell  due,  was  partially  verified  by  the  event. 
(Citing  Compte's  Rendus,  t.  xciii,  p.  827,  t.  xcvi,  p.  1418.)  ''—Gierke's  Hist. 
ofAst.,  3rd  Ed.,  p.  202;  4th  Ed.,  p.  163. 


In  1859  Dr.  R.  Wolf  presented  a  formula  by  which  the  frequency  of  spots 
is  connected  with  thejnotions  of  VenuSj^  the_earth,  Jupiter  and  Saturn,  and 
apparently  exhibited  a  drawing  showing  these  planets  in  conjunction  and  at 
ninety  degrees  from  each  other.  (''Source  and  mode  of  solar  energy." 
Heysinger,  p.  108.) 

William  J.  S.  Lockyer  sums  up  Dr.  Wolf's  sun-spot  period  theory  as 
follows : 

"Dr.  Wolf  was  careful  to  point  out  that  it  was  only  the  mean  length  of 

the  solar  period  that  covered  a  period  of  11^  years,  and  that  the  real  length 

of  any  one  period  might  differ  from  this  value  hy  as  much  as  two  years. 
*     *     * 

"His  attention  was  also  drawn  to  the  fact  that  the  times  of  maxima  did 
not  occur  a  constant  number  of  years  after  a  preceding  minimum,  and  he 
was  led  to  determine  the  mean  time  of  occurrence  of  the  maximum  and  of 
the  minimum  after  the  preceding  maximum,  by  giving  the  7nean  intervals 
as  4.5  and  6.5  years  respectively. 

' '  Further  he  at  first  concluded  that  the  total  spotted  area  for  each  period 
was  nearly  constant,  but,  as  he  later  remarks  (Astron.  Mittheil,  1876,  p.  47 
et  seq.)  this  view  could  not  be  held,  as  these  quantities  not  only  varied  but 
indicated  'eine  bestimme  Gesetz-massigkeit. '  The  length  of  the  period  of 
this  variation  he  gave  as  about  178  years,  which  covered  practically  sixteen 
ordinary  sun-spot  periods  ('11.1111X16=177.7777'). 

"Somewhat  later  Dr.  Wolf  w^as  led  to  suggest  a  shorter  period  of  55.5 
years,  which  comprises  about  five  ordinary  eleven-year  periods. ' ' — Sci.  Am. 
Supp.  24537,  24544,  May  6-13,  1905. 

Miss  Gierke  again  says :  — 

"The  further  inclusion  of  recurring  solar  commotions  within  a  cycle  of 
fifty-five  and  a  half  years  was  simultaneously  (1861)  pointed  out;  and  Her- 
mann Fritz  showed  soon  after  that  the  aurora  borealis  is  subject  to  an 
identical  double  periodicity  (citing  Wolf  Mitth.,  No.  XV,  p.  107)  Olmsted, 
following  Hansteen,  had  already,  in  1856,  sought  to  establish  an  auroral 
period  of  sixty-five  years.     (Smithsonian  Gout.  Vol.  VIII,  p.  37.) 

"The  same  inquirer  detected  besides,  both  for  aurora  and  sun-spots,  a 
"secular  period''  of  222  years  (citing  Hahn,  p.  99,  1877)  and  the  Kew 
Observations  indicate  for  the  latter  oscillations  accomplished  within  twenty- 
six  and  twenty-four  days,  depending  most  likely  upon  the  rotation  of  the 
sun.  (Giting  Rept.  Brit.  Ass.  1881,  p.  518 ;  1883,  p.  418.)  "  Gierke's  Hist. 
Ast.,  3rd  Ed.,  p.  201;  4th  Ed.,  p.  162. 

Professor  Young  says : 

"Professor  R.  Wolf,  of  Zurich,  has  been  especially  indefatigable  in  his 
investigations  upon  this  subject  [periodicity  of  spots]  and  has  succeeded 
in  disinterring  from  all  sorts  of  hiding  places  a  nearly  complete  history  of 
the  solar  surface  for  the  past  one  hundred  and  fifty  years.     *     *     *     and 


^A- 


with  immense  labor  has  combined  them  into  a  consistent  whole,  deducing  a 
series  of  'relative  numbers'  as  he  calls  them,  which  represent  the  state  of 
the  sun  as  to  spottedness  for  every  year  since  1745,  *  *  *  These  rela- 
tive numbers,  as  tested  by  the  most  recent  photographic  results  of  De  La  Rue 
and  Stewart,  are  found  to  be  approximately  proportional  to  the  area  covered 
by  the  spots.  We  give  on  the  opposite  page  a  figure  deduced  from  the 
numbers,  published  by  Wolf  in  1877  in  the  IMemoirs  of  the  Roved  Astronom- 
ical Society  and  showing  their  course  year  by  year  since  1772,  The  hori- 
zontal divisions  denote  years,  and  the  height  of  the  curve  at  each  point 
gives  'relative  number'  for  the  date  in  question.  For  example,  in  1870, 
about  the  middle  of  the  j^ear,  the  relative  number  was  140,  while  early  in 
1879  it  ran  as  low  as  3, "  p.  147:*  *  *  "Our  diagram  *  *  *  only 
goes  back  to  1772,  but  Wolf's  investigations  reach  to  1610,  and  he  gives,"  in 
the  paper  from  which  were  derived  the  numbers  used  in  constructing  our 
diagram  the  following  important  table  of  maxima  and  minima."  (p.  147.) 
*  *  *  (Here  follows  same  table  as  is  given  by  ]\Iiss  Gierke  hereinafter 
copied.) 

''There  is  no  question  of  solar  physics  more  interesting  or  important  than 
that  which  concerns  the  cause  of  this  periodicity,  but  a  satisfaetor3^  solution 
remains  to  be  found.  It  has  6een  supposed  hy  astronomers  of  very  great 
authority  that  the  influence  of  the  planets  in  some  way  produces  it.  Jupiter, 
Venus  and  Mercury  have  been  especially  suspected  of  complicity  in  the  mat- 
ter, the  first  on  account  of  his  enormous  mass,  the  others  on  account  of  their 
proximity,  De  La  Rue  and  Stewart  deduce  from  their  photographic  obser- 
vations of  sun-spots  between  1862  and  1866,  a  series  of  numbers,  which 
strongly  tend  to  prove  that,  when  two  of  the  powerful  planets  are  nearly 
in  line  as  seen  from  the  sun  then  the  spotted  area  is  much  increased.  They 
have  investigated  especially  the  combined  effect  of  Mercury  and  Venus, 
Jupiter  and  Venus,  and  Jupiter  and  Mercury  as  also  the  effect  of  Mercury's 
approach  to,  or  recession  from,  the  sun.  In  all  four  cases  there  seems  to  be 
a  somewhat  regular  progression  of  numbers,  though  much  less  decided  in 
the  third  and  fourth  than  in  the  first  and  second.  The  irregular  variations 
of  the  numbers  are,  however,  so  large  and  the  duration  of  the  observations 
so  short,  that  it  is  hardly  safe  to  build  heavily  upon  the  observed  coinci- 
dences, since  they  may  be  merely  accidental.  An  attempt  to  connect  the 
eleven-year  period  with  that  of  the  planet  Jupiter  also  breaks  down.  While, 
for  a  certain  portion  of  the  time,  there  is  a  pretty  good  agreement  between 
the  sun-spot  curve  and  that  which  represents  the  varying  distance  of  Jupiter 
from  the  .sun,  there  is  complete  discordance  elsewhere.  About  1870  the 
maximum  spottedness  occurred  when  the  planet  was  nearest  the  sun,  but  at 
the  beginning  of  the  century  the  reverse  was  the  case,  Loomis  (who  is  in 
favor  of  inserting  a  sun-spot  maximum  in  1794,  and,  on  this  hypothesis, 
deduces  a  mean  sun-spot  period  of  10  years  in  place  of  11.1)  suggests  that 


the  conjunctions  and  oppositions  of  Jupiter  and  Saturn  may  be  at  the  bot- 
tom of  the  matter,.  These  occur  at  intervals  of  9.93  years,  from  a  conjunc- 
tion to  an  opposition,  or  vice  versa.  But,  when  we  come  to  test  the  matter, 
we  find  that,  in  some  cases,  sun-spot  minima  have  coincided  with  this  allinea- 
tion  of  the  two  planets ;  in  other  cases,  maxima. 

"It  is  indeed,  very  difficult  to  conceive  in  what  manner  the  planets,  so 
small  and  so  remote,  can  possibly  produce  such  profound  and  extensive  dis- 
turbances on  the  sun.  It  is  hardly  possible  that  their  gravitation  can  bo 
the  agent,  since  the  tide  raising  power  of  Venus  upon  the  solar  surface 
would  be  only  about  ^hf  ^^  ^^^^  which  the  sun  exerts  upon  the  earth ;  and 
in  the  case  of  Mercury  and  Jupiter  the  effect  would  be  still  less,  or  about 
Y^-n  of  the  sun 's  influence  on  the  earth. 

"The  sun  (apart  from  the  moon)  raises  a  tide  on  the  deep  waters  of  the 
earth's  equator,  something  less  than  a  foot  in  elevation,  so  that,  making  all 
allowances  for  the  rarity  of  the  materials  which  compose  the  photosphere, 
it  is  quite  evident  that  no  planet  lifted  tides  can  directly  account  for  the 
phenomena.  If  the  sun-spots  are  due  in  any  way  to  planetary  action,  this 
action  must  be  that  of  some  different  and  far  more  subtle  influence." — 
Young,  149  to  151,  Sun,  Aug.  1st,  1881. 

Chambers  says: 

"That  the  period  is  clearly  an  eleven-year  one,  as  has  already  been  stated ; 
(2)  that  it  is  not,  however,  quite  as  simple  in  its  form  as  it  was  at  fii-st 
thought  to  be;  for  in  reality  there  are  two  periods  superposed,  the  one 
rather  more  than  half  a  century  long,  and  the  other  extending  over  the 
eleven  j-ears  already  spoken  of.  We  do  not  possess  early  observations  suffi- 
ciently numerous  and  sufficiently  good  to  enable  lis  to  draw  any  unimpeach- 
able conclusions  as  to  the  nature  of  the  long  period;  we  can  only  be  certain 
that  it  exists.  The  later  labors  of  Wolf,  however,  fixed  that  period  at  55^2 
years.  It  is  a  result  of  this  that,  according  to  Loomis,  a  period  of  compara- 
tive calm  on  the  sun  existed  between  1810  and  1825. 

"Each  maximum  lies  nearer  to  the  minimum  which  precedes  it  than  to 
the  minimum  which  follows  it,  for  the  spots  increase  during  3.7  years  and 
diminish  during  7.4  years.  According  to  De  La  Rue  the  increase  occupies 
3.52  years  and  diminution  7.55  years.  This  concurrence  between  De  La  Rue 
and  AVolf  is  surprising  considering  the  diversity  of  the  methods  which  led 
to  results  almost  identical,  the  one  set  being  based  on  the  number  of  spots, 
and  the  other  on  the  superficial  extent  of  the  spots.     *     *     * 

"The  presence  of  spots  only  in  Zodiacal  regions  led  Galileo  to  suspect  the 
existence  of  some  relations  between  the  spots  and  the  position  of  the  planets; 
but  there  is  in  this  a  mere  surmise,  which  when  it  was  made,  had  nothing  to 
justify  it,  and  it  is  still  impossible  for  us  to  say  anything  for  certain  on  the 
point. 


8 

*' According  to  Wolf,  the  attraction  of  the  planets  or  some  of  them,  is  the 
real  cause  of  the  periodicity  which  u'e  are  dealing  ivith;  that  attraction 
producing  on  the  surface  of  the  solar  globe  true  tides,  which  give  birth  to  the 
spots,  these  tides  themselves  experiencing  periodic  variations  owing  to  the 
periodic  changes  of  position  of  the  celestial  bodies  which  cause  them.  It 
has  even  been  thought  safe  to  assert  that  the  fact  of  the  principal  period 
coinciding  with  the  revolution  of  Jupiter  is  of  momentous  significance ;  but 
this  coincidence  seems  purely  accidental,  and  no  certain  conclusion  can  be 
dra^^Ti  as  to  this  matter.  The  influence  of  Mercury  and  Venus  would  per- 
haps be  much  more  potent,  for  their  distance  from  the  sun  is  not  very  great, 
and  this  should  render  their  influence  more  sensible.  On  the  other  hand 
their  masses  appear  to  be  too  small  to  be  capable  of  producing  any  suffi- 
cient effect. 

"De  La  Rue,  Balfour  Stewart,  and  Lowy  most  perserveringly  studied 
this  point  of  solar  physics.  Tliey  seem  to  have  arrived  at  the  conclusion 
that  the  conjunctions  of  Venus  and  Jupiter  do  exercise  a  certain  amount  of 
influence  on  the  number  of  spots  and  on  their  latitude ;  and  that  this  influ- 
ence is  less  considerable  when  Venus  is  situated  in  the  plane  of  the  solar 
equator.  At  any  rate  it  is  a  fact  that  a  great  number  of  the  visible  inequali- 
ties in  a  duly  plotted  curve  of  the  spots  do  really  correspond  to  special 
positions  of  these  two  planets. 

"In  order  to  determine  with  more  precision  these  coincidences  and  the 
importance  which  attaches  to  them,  De  La  Rue  extended  his  inquiries.  He 
separately  analyzed  many  different  groups  of  spots,  selecting  for  his  pur- 
pose more  particularly  those  of  which  the  observations  happened  to  have  been 
specially  continuous  and  complete,  giving  a  preference  moreover  to  those 
which  had  been  observed  in  the  central  portions  of  the  sun's  disc.  From 
an  investigation  of  794  groups  De  La  Rue  arrived  at  the  following  conclu- 
sions: (1)  If  we  take  a  meridian  passing  through  the  middle  of  the  disc 
and  represented  by  a  diameter  perpendicular  to  the  equator,  we  find  that 
the  mean  size  of  the  spots  is  not  the  same  with  regard  to  that  meridian.  It 
appears  certain  that  the  correction  required  for  perspective  does  not  suffice 
to  explain  this  difference ;  and  that  another  element  must  be  introduced  in 
order  to  secure  that  the  apparent  dimensions  of  the  spots  may  be  the  same 
on  both  sides.  We  do  not  yet  possess  a  very  clear  explanation  of  this  fact; 
but  the  most  probable  is  this : — that  the  spots  are  surrounded  by  a  project- 


ing  bank,  which  seems  to  disappear  in  part  during  their  transit  across  the 
sun.  This  bank  is  more  elevated  on  the  preceding  than  on  the  following 
side;  accordingly  the  spots  ought  to  seem  smaller  when  they  are  in  the 
eastern  half  of  the  disc  larger  when  they  are  in  the  western  half ;  for  in  the 
first  position  the  observer's  eye  meets  an  elevated  obstacle,  which  hides  a 
portion  of  the  spot  itself.  (2)  De  La  Rue  specially  studied  the  spots 
observed  at  the  times  when  the  planets  Venus  and  Mars  were  at  a  heliocen- 
tric distance  from  the  earth  equal  to  0,  90,  180  and  270  degrees,  and  arrived 
at  this  result ;  the  spots  are  larger  in  the  part  of  the  sun  which  is  away  from 
Venus  and  Mars,  and  they  are  smaller  on  the  side  on  which  these  planets 
happen  to  be.  The  same  result  was  obtained,  whether  Carrington's  figures 
or  the  Kew  photographs  were  employed.  (3)  Meanwhile  it  does  not  appear 
that  Jupiter  emits  any  similar  influence.  This  influence  should  be  easily 
perceived,  for  if  we  calculate  the  action  of  the  planets  in  the  way  that  we 
calculate  the  tides,  treating  it  as  directly  proportional  to  the  masses  and 
inversely  proportional  to  the  cubes  of  the  distances,  the  influence  of  Jupiter 
should  greatly  outweigh  that  of  Venus. 

' '  Wolf  thought  he  had  noticed  traces  of  some  influence  being  exerted  by 
Saturn,  but  this  remains  altogether  without  confirmation. 

"De  La  Rue  noticed  thai  large  spots  are  generally  situated  at  extremities 
of  the  same  diameter.  This  law  also  often  applies  to  the  development  of 
large  prominences.  The  coincidence  agrees  well  with  the  theory  that  there 
exists  on  the  sun  some  action  resemhling  that  of  our  tides." — Story  of  the 
Solar  System,  Chambers,  p.  51  et  seq.,  Appleton,  N.  Y.,  1904. 

Flammarion  takes  up  the  argument  based  on  the  influence  of  Jupiter  and 
disposes  of  it  as  follows : 

' '  What  may  be  the  cause  of  this  motion  of  the  solar  surface  ? 

* '  This  cause  may  be  in  the  interior  of  the  sun.  It  might  also  be  exterior 
to  him. 

"  If  it  is  in  the  interior  of  the  solar  body,  it  would  not  be  easily  discovered. 

"If  it  be  exterior,  the  first  idea  which  suggests  itself  is  to  seek  for  it  in 
some  combination  of  planetary  motions. 

"Among  the  different  planets  of  the  system  there  is  one  which,  from  its 
importance,  first  presents  itself  to  us,  and  it  is  found  that  the  duration  of 
its  revolution  round  the  sun  approaches  closely  to  the  preceding  period. 
Our  readers  have  already  named  Jupiter,  of  which  the  diameter  is  only  ten 
times  smaller  than  that  of  the  solar  colossus,  and  of  which  the  mass  is  equiva- 
lent to  a  thousandth  of  that  of  the  central  star.  It  revolves  round  the  sun 
in  11.85  years. 

"During  the  course  of  its  revolution  its  distance  from  the  sun  is  subject 
to  a  perceptible  variation.  This  distance,  which  is,  on  the  average  5.203 
(that  of  the  earth  being  one)  sinks  at  the  perihelion  to  4.950  and  rises  at  the 
aphelion  to  5.456.     The  difference  between  the  perihelion  and  aphelion  dis- 


10 

tance  is  0.506 — that  is  to  say,  a  little  more  than  half  the  distance  from  the 
earth  to  the  sun,  or  about  47  millions  of  miles.  This  is  rather  considerable. 
Revolving  thus  round  the  sun,  Jupiter  exercises  on  him  an  attraction  easily 
calculated,  and  constantly  displaces  his  center  of  gravity,  which  can,  conse- 
quently, never  coincide  with  the  center  of  figure  of  the  solar  sphere,  and  is 
always  found  drawn  eccentrically  towards  Jupiter.  The  attraction  of  the 
other  planets  prevents  this  action  from  being  regular,  but  it  can  not  prevent 
it  from  being  predominant. 

"It  might  be  thought  that  this  motion  of  the  solar  mass  should  be  inter- 
preted for  us  by  the  spots,  and  that  it  might  have,  for  example,  a  maximum 
of  spots  when  Jupiter  attracts  more,  or  attracts  less,  the  solar  center.  If  we 
had  here  the  cause  of  the  periodicity  of  the  spots,  this  periodicity  should  be 
11.85  years.  But  it  is  shorter.  While  Jupiter  returns  to  his  perihelion 
only  after  11.85  years,  the  maximum  of  spots  returns  very  irregularly,  but 
on  the  average  after  11.11  years — that  is  to  say,  Ti  hundredths  of  a  year  or 
270  days  sooner.  This  number  comes  from  a  discussion  of  all  the  observa- 
tions. Does  there  exist  in  the  solar  system  a  second  cause  which  obliges  a 
phenomenon  to  advance  thus  on  the  perihelion  of  Jupiter  ?  Venus  revolves 
round  the  sun  in  225  days,  and  about  every  225  days  meets  the  radius  vector 
of  Jupiter.  The  earth  revolves  in  365  days,  and  meets  the  radius  vector  of 
Jupiter  every  399  days.  These  two  planets  certainly  act  on  the  sun  in  the 
same  way  as  the  giant  planets,  but  with  less  intensity.  If  this  common 
action  were  expressed  by  an  increase  of  spots  we  should  see  in  the  fluctua- 
tions of  the  solar  spots  combinatons  of  the  period  of  11.85  of  Jupiter  with 
that  of  one  year  for  the  earth,  of  0.62  for  Venus,  and  of  0.24  for  Mercury. 
Unfortunately,  this  combination  does  not  appear  to  produce  the  observed 
effect. 

"Whether  it  be  the  perihelion  or  the  aphelion  of  Jupiter  which  causes  the 
maximum  of  solar  spots,  these  maxima  should  always  coincide  with  the  same 
positions.  But,  on  the  contrarj^,  each  revolution  of  Jupiter  adds  the  differ- 
ence of  0.74  which  we  have  just  noticed,  and  at  the  end  of  a  certain  time,  of 
thirteen  to  fourteen  revolutions,  the  positions  are  reversed.  We  must,  then, 
although  with  regret,  give  up  Jupiter. 

' '  Whatever  may  be  the  relation  which  exists  between  the  two  periods,  the 
connection  is,  then,  purely  accidental,  for  we  cannot  logically  admit  that 
the  same  causes  produce  contrary  effects  and  that  the  perihelion  sometimes 
induces  a  minimum  and  sometimes  a  maximum. 

"However  let  us  dismiss  the  idea  of  the  variation  of  the  distance  of  Jupi- 
ter and  consider  only  its  imaginary  circular  revolution.  Let  us  suppose 
that  the  variation  of  distance  does  not  act  perceptibly.  The  fact  still 
remains  that  Jovian  attraction  makes  the  center  of  gravity  turn  round  his 
center  of  figure  in  11.85  years.     Are  the  spots  always  on  the  radius  vector  of 


11 

Jupiter?  No,  the  earth  crosses  this  radius  vector  every  thirteen  months, 
and  we  do  not  see  more  spots  on  that  solar  hemisphere  than  on  the  opposite 
hemisphere.  IMoreover  the  sun  rotates  on  itself  in  26  days  and  would  bring 
thes6  spots  in  view  of  the  earth,  since  they  turn  with  the  solar  surface. 
Under  whatever  aspect  we  discuss  the  question,  we  are,  then,  led,  in  spite  of 
ourselves,  to  eliminate  the  action  of  Jupiter.  It  is  the  same  and  with  much 
stronger  reason  as  regards  all  the  other  planets. 

"It  is  difficult  to  conceive  how  the  planets  which  are  so  small  and  so  dis- 
tant could  produce  in  the  sun  disturbances  so  profound  and  so  extensive.  It 
is  scarce!}'  possible  that  it  should  be  their  gravitation  which  acts,  considering 
that  the  attractive  power  of  Venus  on  the  solar  surface  would  be  about  -^^^ 
of  that  which  the  sun  exercises  on  the  earth ;  and  in  the  case  of  Mercury  and 
Jupiter  the  effect  would  be  still  less,  about  ^^\^  of  the  influence  of  the  sun 
on  the  earth.  The  sun,  considered  apart  from  the  moon,  raises  on  the  deep 
waters  at  the  earth's  equator  a  tide  of  a  little  less  than  13  inches  in  height, 
so  that,  taking  into  account  the  rarefaction  of  the  substance  of  which  the 
photosphere  is  composed,  it  is  very  evident  that  any  tide  produced  by  n 
planet  can  not  directly  explain  the  phenomena.  If  the  solar  spots  are  due 
in  any  way  to  planetary  action,  this  action  must  be  that  of  a  different  and 
much  more  subtle  influence." — Flammarion  Pop.  Ast.,  pp.  285-287. 

These  authors  summarize  the  efforts  of  astronomers  to  ascertain  the 
causes  of  the  sun-spots  and  of  their  waxing  and  waning  and  of  the  efforts 
to  connect  therewith  the  movements  of  some  of  the  planets.  It  has  been 
shown  that,  beginning  with  Galileo  and  down  to  the  efforts  of  De  La  Rue, 
Stewart  and  Lowe,  they  partially  examined  for  brief  periods  the  effects 
upon  the  motion  of  the  sun  of  some  of  the  planets,  and  abandoned  their 
efforts  because  they  thought  that  the  planets  were  too  small  and  remote; 
and,  that  such  influences  were  inadequate  and  indeterminate  as  a  cause. 

I  present  herein  some  facts  and  tabulated  calculations  based  upon  long 
periods  of  time — 28  centuries — to  show  that  a  sufficient  physical  cause  of 
the  sun 's  disturbance  is  to  be  found  in  the  movements  and  attraction  of  the 
four  great  planets  Jupiter,  Saturn,  Uranus  and  Neptune;  and  that  the 
physical  disturbance  of  the  mass  and  motion  of  the  sun  by  the  mass  and 
motion  of  those  planets  is  synchronous  with  and  proportionately  variable 
with  all  of  the  observed  solar  and  terrestrial  phenomena  for  which  solar 
action  is  now  held  responsible.  That  as  the  mass  and  motion  of  the  planets 
is  concentrated  in  one  direction  upon  the  sun  its  excitement  reaches  a  maxi- 
mum; and  as  their  masses  and  motions  are  dispersed  that  excitement  is 
allayed  and  reaches  a  minimum ;  and  that  such  concentration  and  dispersion 
coincides  in  time  and  force  with  the  facts  reached  by  induction  from  obser- 
vations upon  sun-spots,  prominences,  auroras,  coronas,  magnetic  declina- 
tion, change  of  form  of  the  sun,  and  other  effects  of  solar  activity. 


12 

R.  A.  Proctor  rrave  the  physical  effects  of  the  planets  upon  the  sun  in  his 
' '  Old  and  New  Astronomy ' '  as  follows : 

*'(713)  :  The  sun's  mass  so  enoraiously  exceeds  that  of  all  the  planets 
taken  together,  that  he  is  capable  of  swaying  their  motion  without  being 
himself  disturbed.  He  is  not  indeed  quite  fixed.  We  know  from  Newton's 
third  law  that  whatever  force  the  sun  exerts  on  any  planet,  the  planet  exerts 
precisely  the  same  force  on  hira;  but  then  he  is  so  massive  that  the  pull 
which  compels  a  planet  to  circle  round  the  sun  displaces  him  very-^  slightly." 
[In  a  note  to  this  he  says:] 

"Not,  however,  quite  so  slightly  as  Sir  John  Herschel  asserts  in  the  fol- 
lowing oft-quoted  passage : 

"If  he  pulls  the  planets,  they  pull  him  and  each  other;  but  siich  family 
struggles  affect  him  but  little.  Thry  amuse  them  he  proceeds  quaintly,  but 
don't  disturb  him.  As  all  the  gods  in  the  ancient  mythology  hung  dangling 
from  and  tugging  at  the  golden  chain  which  linked  them  to  the  throne  of 
Jove,  but  without  power  to  draw  him  from  his  seat,  so,  if  all  the  planets 
were  in  one  straight  line  and  exerting  their  joint  attractions,  the  sun — 
leaning  a  litttle  back  as  it  were  to  resist  their  force — would  not  be  disturbed 
by  a  space  equal  to  his  own  radius ;  and  the  fixed  center,  or,  as  an  engineer 
would  call  it,  the  center  of  gravity  of  our  system,  would  lie  still  far  within 
the  sun 's  globe. ' ' 

Proctor  proceeds  as  follows : 

"The  distance  of  the  center  of  gravity  of  the  whole  row  of  bodies  from 
the  sun's  center  can,  of  course,  be  easily  determined  with  precision  in  the 
case  imagined  by  Sir  John  Herschel,  (all  the  planets  in  one  straight  line  on 
the  same  side  of  the  sun).  But  in  such  an  inquiry  we  can  neglect  minutiae 
and  need  consider  only  the  four  primary  planets,  while  we  may  regard  the 
distance  of  any  one  of  these  planets  from  the  center  of  gravity  of  the  whole 
system  as  appreciably  equal  to  the  distance  from  the  sun's  center  the  differ- 
ence of  these  distances  being  exceedingly  small  compared  with  either. 

"Calling  the  sun's  m.ass  1,  and  the  distance  of  the  center  of  gravity  of 
the  sun  from  the  center  x,  we  find,  taking  moments  about  the  common  center 
of  gravity, 
Sun's  moment=Jupiter's4-Saturn's-(-Uranus'+Neptune's,  or 

1  v.    482,700.000  I  885.000,000  ■1,779,830,000.  2.788,500.000 
'^       1,048   ~r   3.500    I"   22,600   "T   19.380 

).  e.,  x=460,0004-253,000+79,000+145,000=937,000  in  round  numbers. 

"Showing  that  the  center  of  gravity  of  the  whole  solar  system  would, 
in  the  case  supposed,  lie  more  than  half  a  million,  more  exactly,  505,000 
(937,000—432,000)  miles  from  the  sun's  surface."— Procf or 's  Old  and  New 
Astronomy ,  p.  304. 


13 

Again  he  says : 

"  (759)  :  The  orbit  of  the  sun  is  complex  in  shape  since  it  is  compounded 
of  the  circling  motions  which  would  severally  result  from  the  action  of  the 
different  planets.  "We  may  neglect  the  movements  due  to  the  four  inner 
planets  as  insignificant  in  range,  though  of  course  in  any  exact  computation 
they  would  have  to  be  taken  into  account.  Taking  the  four  giant  planets 
separately,  we  find  from  what  is  shown  in  the  note  to  Art.  713  that  the  sun 
would  describe  (1)  if  Jupiter  alone  were  considered  a  circle  (slightly  eccen- 
tric but  not  appreciably  elliptical)  round  the  center  of  gravity  of  Jupiter's 
mass  and  his  own,  once  in  Jupiter's  period,  the  radius  of  the  orbit  being 
about  460,000  miles ;  (2)  considering  Saturn  alone,  a  circle  round  the  center 
of  gravity  of-  Saturn 's  mass  and  his  own,  once  in  Saturn 's  period,  the  radius 
of  the  orbit  being  253,000  miles;  (3)  considering  Uranus  alone,  a  circle 
79,000  miles  in  radius,  round  the  center  of  gravity  of  Uranus'  mass  and 
his  own,  once  in  Uranus'  period;  and  (4)  considering  only  Neptune  a  circle 
145,000  miles  in  radius  round  the  common  center  of  gravity  of  his  o^\ti  mass 
and  Neptune's  in  Neptune's  period.  The  actual  motion  of  the  sun  would 
be  that  compounded  of  these  four  circling  motions  with  their  different 
periods,  and  such  smaller  motions  as  would  result  from  the  disturbing 
actions  of  the  several  smaller  planets,  satellites,  asteroids,  etc.  The  curve 
would  be  exceedingly  complicated  even  if  we  considered  only  the  motions 
due  to  the  four  giant  planets.  Here  we  need  only  note  that  the  greatest 
range  of  the  sun  from  the  common  center  of  gravity  of  the  solar  system  can 
never  exceed  940,000  miles,  and  ver^^  seldom  approaches  that  amount." — 
Proctor  Old  and  New  Astronomy,  p.  323. 

' '  The  total  mass  of  the  solar  system  may  be  taken  as  follows : 
"  (Earth's  mass=l.) 

Sun 332,262 

Jupiter 317 

Saturn 95 

Neptune 17.4 

Uranus 14.6 

Earth 1.0 

Venus   .8 

Mars .11 

]\Iercury .06 

Satellites .20 

]\Iinor  planets .25 

Total 332,708.42." 

— Appendix,  Note  A,  "Visible  Universe"  Gore. 

Taking  the  latest  accepted  figures  I  find  the  mass  effect  of  the  eight  great 
planets  upon  the  sun  to  be  as  follows : 


3r  vS/^s^^w^-t^ 


14 

^ Sun's  mass  equals  1.) 

JiilMter's  inass^Yi)^--35 ,  mean  distance  483,000,000  miles;  divided  by 
mass  plus  oue=461,010  miles,  which  is  the  distance  by  which  tlie  center  of 
irravity  of  the  sun  is  displaced  by  the  attraction  of  Jupiter. 

Saturn's  mass=3-^,  mean  distance  886,000,000;  displacement=252,92G 
miles. 

Uranus'  raass=2276o"'  ^^^'^^  distance  1,781,900.000;  di.splacement=78,287 
miles. 

Neptune's  mass^j^^^,  mean  distance  2,791,600,000;  displacement= 
143.151  miles. 

Total  displacement  of  center  of  gravity  of  sun  (or  rather  distance  of  cen- 
ter of  gravity  of  solar  system  from  sun's  center)  by  four  great  planets  when 
all  pulling  in  one  line  on  the  same  side  equals  935,374  miles. 

Earth's  mass=33^^0Q,  mean  distance  92,900,000  miles;  displacement= 
280  miles. 

Venus'  mass=  ^^^j^,  mean  distance  67,200,000  miles;  displacement= 
174  miles. 

Mars'  mass=^g-^g|-^ ,  mean  distance  141,500,000;  displacement=45  miles. 

Mercury's  mass=  g  33^  ^^q  ,  mean  distance  36,000,000;  displacement=5 
miles. 

Total  displacement  effected  by  last  four  planets,  under  same  conditions, 
'i^'b^^         504  miles. 

^S^k>tC>  Therefore  the  mere  pulling  influence  of  the  last  four  planets  may  be 

,      /■7<r'i-  6        neglected  as  comparatively  insignificant. 

^     y-^^^^  ^  l^         But  any  calculations  based  upon  the  ancient  idea  of  the  sun's  immobility 

will  be  misleading.     For  the  purposes  of  this  first  chapter  I  will  assume 

''      •  that  the  sun  is  moving  through  space  from  heliocentric  longitude   90° 

/      31  b^^  towards  270°  at  the  speed  of  eleven  miles  a  second;  that  being  the  most 

conservative  speed  now  stated  by  astronomers  and  it  is  entirely  sufficient 

-L^    /7'  t?  -^"^  ^^^^^  exposition.     The  question  of  the  actual  velocity  of  the  sun  in  its 

journe}'  to  its  apex  is  involved  in  the  next  chapter. 

All  references  herein  to  longitudes  are  to  heliocoitric  longitude  unless 
otherwise  expressed. 

I  have  calculated  and  used  tables  of  the  heliocentric  mean  longitude,  to 
the  nearest  degree,  of  the  eight  planets  on  the  first  day  of  January  for  each 
year  back  to  1000  B.  C.  In  such  an  investigation  as  this  greater  accuracy 
is  not  necessary. 

Upon  these  tables  I  have  based  the  computations  in  Tables  I,  II,  III, 
appendix  and  the  other  tables  in  the  body  of  this  pamphlet. 

A  few  instances  will  illustrate  their  use. 

On  January  1st,  1843,  the  heliocentric  longitude  of  the  four  great  planets 
was  as  follows:   Jupiter,  307°;  Saturn,  288°;  Uranus,  4°;  Neptune,  321°. 


V 


'1     r-7 


15 

The  resultant  of  their  combined  attraction  was  to  drive  the  sun  out  of  its 
course  870,000  miles  from  the  center  of  gravity  of  the  solar  system  which 
was  that  distance  away  from  the  center  of  the  sun  in  the  direction  308° 
longitude.  This  distance  is  the  vector  and  it  is  the  hypothenuse  of  a  tri- 
angle of  which  one  side  is  the  perpendicular  distance  of  the  sun — east  or 
west — from  the  line  formed  by  the  progress  of  the  center  of  gravity  of  the 
system ;  the  other  side  shows  the  distance  at  which  the  center  of  the  sun  is 
ahead — plus — or  behind^-minus — of  center  of  gravity  of  the  system, 
measured  in  the  path  of  the  center  of  gravity  and  being  plus  or  minus  as 
respects  the  solar  apex.  The  two  sides  of  the  triangle  give  the  ordinates  of 
the  sun's  position  relative  to  the  center  of  gravity  of  the  solar  system  and 
to  the  solar  apex. 

For  the  years  18-44  to  1851  the  positions  of  the  planets  and  their  effect 
upon  the  sun  are  given  by  Table  II.  Let  us  assume  the  fact  that  the  center 
of  gravity  of  the  solar  system  (hereinafter  called  the  center  of  gravity) 
follows  a  right  line  in  the  journey  towards  the  solar  apex  and  that  the  direc- 
tion of  that  line  is  from  90°  towards  270°  ;  then,  by  plotting  the  ordinates 
of  the  sun 's  position  and  the  position  of  the  center  of  gravity  of  the  system 
and  joining  them  with  the  vector  lines,  for  the  years  1843  to  1851,  we  will 
get  the  path  pursued  by  the  sun  during  those  years.  We  can  assume  arbi- 
trarily for  the  yearly  advance  of  the  sun  one  inch  per  year  and  plot  the 
ordinates  on  a  scale  of  200,000  miles^l  inch. 

From  such  a  plat  we  find  that  the  sun's  path  through  space  for  those 
years  is  a  curved  line  on  the  west  side— towards  heliocentric  longitude  180° 
— of  the  straight  line  described  by  the  advance  of  the  center  of  gravity  of 
the  system  during  that  period ;  and  that,  about  the  date  1850.2,  the  curved 
line,  formed  by  the  advance  of  the  center  of  the  sun,  crossed  the  straight 
line ;  formed  by  the  center  of  gravity  of  the  system ;  and,  at  the  end  of  the 
year  1850  the  sun's  center  had  reached  a  point  about  40,000  miles  to  the 
east  side  of  the  straight  line.  That  during  this  period  the  sun  was  in  the 
rear  of  the  center  of  gravity  until  about  the  middle  of  the  year  1845  after 
which  it  was  in  advance  of  the  center  of  gravity.  Figure  1  shows  a  plotting 
for  the  last  18  years. 

Plotting,  from  the  figures  in  Table  II,  the  path  of  the  sun's  center  and 
of  the  center  of  gravity  of  the  system  for  each  year — from  1480  to  1910, 
with  the  vector  lines  connecting,  we  will  observe  the  following  facts: 

The  path  of  the  sun  through  space,  following  the  general  direction  to  its 
apex  from  90°  to  270°,  is  a  serpentine  curve  alternating  on  either  side  of  a 
straight  line  produced  through  space  by  the  progress  of  the  center  of 
gravity  of  the  solar  system.  This  curved  path  is  caused  by  the  varying  posi- 
tions of  the  planets  and  by  the  combined  attraction  of  their  mass  and 
motion. 


16 

The  extreme  distanee  of  the  center  of  the  sun  from  the  line  of  the  center 
of  ^'ravity  is  reached  when  the  phinets  are  in  closest  conjunction  and  may 
at  times  amount  to  934,000  miles. 

The  sun,  relative  to  the  direction  of  its  motion  is  alternately  in  advance  of 
or  in  the  rear  of  the  center  of  gravity  of  the  system,  sometimes  to  the  extent 
of  934.000  miles  and  sometimes  but  a  very  few  miles.  The  sun  is  therefore 
retarded  or  assisted,  in  its  progress  through  space  by  the  position  of  the 
planets  and  the  direction  and  amount  of  their  combined  attraction. 

These  alternating  conditions  are  periodical  and  the  periods  recur  and  are 
caused  as  follows :  Jupiter  is  in  conjunction  with  Saturn  every  19.855 
yeare ;  with  Uranus  every  13.81  years ;  with  Neptune  every  12.78  years.  All 
four  are  nearly  in  conjunction  as  follows:  Jupiter  with  Neptune  every 
38.345  years ;  Jupiter  with  Saturn  every  39.71  years ;  Jupiter  with  Uraiuis 
every  41.43  years.  So  that  about  every  40  yeara  or  thereabouts  after  or 
before  a  perfect  conjunction  these  planets  would  again  be  nearly  in  line. 

But  they  make  a  more  perfect  conjunction  as  follows :  Jupiter  with 
Saturn  every  178.695  years;  Jupiter  with  Neptune  every  178.944  years; 
Jupiter  with  Uranus  every  179.553  years. 

Assuming  the  planets  to  have  started  even  from  zero,  by  combination  of 
these  periods  we  ought  to  get  a  series  of  periodical  conjunctions  more  or 
less  perfect  every  40,  138,  178,  and  218  years  and  so  on. 

The  four  great  planets  were  in  very  close  conjunction  about  September 
26,  1306.  That  is  the  closest  position  on  line  with  the  sun  in  which  I  have 
found  them  as  far  back  as  1000  B.  C.  On  September  26,  1306  their  longi- 
tudes were  Jupiter,  231°;  Saturn,  217°;  Uranus,  227°;  Neptune  231°. 
The  resultant  of  their  attraction  w^as  in  the  direction  226.5°  and  the  dis- 
tance of  the  center  of  gravity  of  the  system  from  the  sun's  center  was 
934,000  miles. 

In  the  early  part  of  1307 — my  tables  call  for  April  30th — all  of  the  eight 
great  planets  were  gathered  nearly  on  line  with  the  sun  between  longitudes 
213°  and  258°.  (My  calculations  are  based  upon  mean  longitude.  No 
account  is  taken  of  the  exact  positions  of  Mercury  or  Mars.  Their  pull 
value  is  negligible  so  it  does  not  matter  where  they  were  exactly  on  that 
date.) 

We  can  use,  therefore,  January  1,  1307  as  a  zero  epoch  whence  we  can 
reckon,  backward  or  forward,  for  recurrence  of  epochs  of  conjunction,  of 
the  four  great  planets. 

But  it  is  impossible  to  completely  describe,  in  words  merely,  the  results 
to  be  obtained  from  the  figures  in  Table  II  of  the  appendix.  They  should 
be  plotted  l)y  the  reader — such  a  plat  is  too  bulky  to  print.  I  used  12  yards 
of  cross  section  paper  ten  inches  wide  to  plat  from  1480  to  1910.  I  assumed 
an  arbitrary  scale  of  1  inch  per  year  to  represent  the  advance  of  the  sun  to 
its  apex  at  any  speed,  and  a  scale  of  one  inch  ec^ual  to  200,000  miles  to  plot 


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17 

the  positions  of  the  centers  of  gravity,  the  center  of  the  sun,  and  the  length 
and  direction  of  the  vector  line  joining  those  centers.  As  the  advance  of 
the  sun  is  not  represented  to  scale  the  positions  of  the  center  of  gravit}^  will 
lead  to  confusion  unless  that  fact  is  kept  in  mind.  With  this  plat  we  obtain 
an  exaggerated  curve  for  the  path  of  the  sun's  center  similar  to  the  exag- 
gerated curve  of  an  engineer's  line  of  levels  where  two  scales  are  used  one — 
horizontal — and  arbitrary — the  other — vertical — and  true. 

I  will  assume  that  the  reader  has  made  such  a  plat  or  that  Figure  ] 
answers  as  an  illustration.  He  will  see  that,  when  the  vector  line  coincides 
with  the  path  of  the  center  of  the  gravity,  the  sun,  or  the  resultant  of  the 
planets  attractions,  is  ahead  or  astern  with  regard  to  the  journey  to  the  solar 
apex.  The  exact  moment  is  determined  when  the  curved  line  of  the  sun's 
center  crosses  the  straight  line  generated  by  the  center  of  gravity.  If  the 
sun  is  ahead  of  the  resultant,  or  center  of  gravity,  then  the  sun  will  be 
exerting  its  motive  power  to  pull  the  planets  along  its  path  and  to  overcome 
their  resistance.  If  the  center  of  gravity  is  ahead  of  the  sun  then  the 
planets  are  exerting  their  motive  power  to  pull  the  sun  along  its  path.  This 
results  naturally  from  the  operation  of  the  Newtonian  law  that  attractions 
are  equal  and  opposite  and  the  general  motion  of  the  solar  system  is  always 
in  one  direction  namely  towards  the  apex. 

During  the  period  of  a  great  year,  namely  every  178  years,  or  from  the 
perfect  conjunction  of  the  planets  to  another  like  epoch,  we  will  find  several 
minor  periods  marked  by  the  condition  that,  for  a  short  period  of  yeare,  the 
sun  is  towing  the  planets ;  and,  during  the  next  short  period,  the  planets 
are  towing  the  sun.  These  shorter  periods  vary  one  from  another  as  the 
planets  are  concentrated  or  dispersed  from  time  to  time  exerting  more  or  less 
force  in  opposition  to  the  sun.  Thus  we  get  what  we  may  call  seasons  in 
this  great  year  period — applying  old  terms  to  new  uses. 

The  beginning  and  ending  of  each  period  which  is  marked  by  sun  or 
planets  being  in  tow,  is,  of  course,  determined  by  the  date  when  the  vector 
line  from  the  sun's  center  to  the  center  of  gravity  is  at  right  angles  to  the 
path  of  the  center  of  gravity. 

Therefore,  in  the  determination  of  these  periods,  the  beginning,  the  ending 
and  the  maximum  of  each  period  are  subjects  of  precise  calculation  and  may 
be  graphically  shown  by  the  plat. 

I  will  assume  for  the  present,  giving  reasons  later  on,  that  the  period  dur- 
ing which  the  sun  is  in  the  lead  pulling  the  planets  along  its  path  is  a  period 
of  sun-spot  maxima;  and  that  the  period  during  which  the  planets  are  in 
the  lead — that  is  when  the  center  of  gravity  is  in  the  lead — is  a  period  of 
sun-spot  minimum. 

The  plat  made  therefrom  and  the  Table  II  show  that  epochs  of  perfect 
conjunction  occurred  in  1486,  1665  and  1844 ;  and  that,  in  1486.35,  1663.65 
and  1841.1  the  sun  was  crossing  the  line  of  the  center  of  gravity  towards 


18 

the  west  namely  towards  heliocentric  longitude  180° ;  in  each  instance  being 
in  tow  of  the  planets  astern.  These  dates  may  then  be  taken  as  epochs,  or 
definite  points  of  commencement  of  epochs,  of  similar  solar  and  planetary 
conditions.  Arranging  the  ordinates  of  the  sun's  motion  as  in  Table  III, 
we  can  examine  the  parallel  conditions  during  these  three  periods,  two  of 
which  are  completed;  these  periods  covering  our  precise  records  of  solar 
activity. 

From  Table  III  and  the  plat  it  will  be  seen  that  the  ordinates  of  the  sun 's 
path,  as  it  crosses  the  path  of  the  center  of  gravity,  from  side  to  side  con- 
form very  nearly  in  every  detail.  Yet  there  is  that  difference,  between 
similar  conditions,  which  would  be  expected  from  the  more  or  less  perfect 
conjunctions  of  the  planets  and  from  the  fact  that  such  conjunctions  never 
consecutively  occur  in  the  same  part  of  the  heavens.  As  we  have  seen,  at 
the  head  of  the  three  columns  of  Table  III,  the  sun  was  crossing  to  the  west 
of  the  line.  In  1489  the  middle  ordinate  of  the  western  curve  w^as  540,000 ; 
in  1667  it  was  715,000  miles ;  in  1845  it  was  820,000.  In  1493.24  the  sun 
was  crossing  the  line  to  the  east  side,  or  towards  the  first  point  in  Aries  and 
it  was  so  crossing  in  1671.95  and  in  1850.3,  each  time  commencing,  as  we 
will  see,  a  sun-spot  maximum  period.  It  began  a  new  maximum  period  in 
1504.07,  1681.9  and  1859.6 ;  the  intervals  between  these  two  sets  of  periods 
being  10.83  years,  9.95  years  and  9.3  years  respectively.  So  that  while 
there  was  complete  parallelism  between  these  great  year  seasons  there  were 
also  systematic  differences. 

We  are  now  ready  to  examine  these  tables  in  connection  with  observed 
and  tabulated  events  connected  with  the  sun  principally  its  sun-spot  maxima 
and  minima. 

In  the  tabulation  of  sun-spot  periods  following  the  accepted  table  of  sun- 
spot  maxima  and  minima  was  taken  from  IMiss  Gierke's  History  of  Astron- 
omy, Appendix. 

I  have  paralleled  the  minima  column  with  a  column  giving  the  dates  con- 
stituting the  periods  during  which  the  planets — the  center  of  gravity — was 
in  the  lead  of  the  sun  and  pulling  it  along  its  path.  This  column  is  also 
paralleled  with  a  column  of  dates  when  the  center  of  gravity  of  the  system 
was  directly  in  the  lead ;  the  sun  being  astern  like  a  ship  being  towed  into 
harbor.  Alongside  that  column  is  another  showing  the  intervals  in  years 
between  the  latter  epochs.  This  last  column  shows  the  same  irregularity 
which  characterizes  the  generally  accepted  intervals  between  periods  of 
sun-spot  maxima  and  minima  and  in  this  case  it  constitutes  the  strongest 
item  of  evidence  of  the  fact  that  this  table,  derived  in  this  manner  entirely 
from  data  ahsolutely  free  from  a  douhtful  assumption  or  theory,  is  in  fact  a 
table  which  demonstrates  the  relation  of  cause  and  efl'eet  between  solar 
agitation  and  planetary  position  and  motion.  The  same  system  of  tabula- 
tion follows  for  the  sun-spot  maxima. 


19 


TABLE    OF    SUN-SPOT    MINIMA. 


Sun-spot  Minima 

(from  Agnes  Clerlte's 

History  of  Astronomy) 

Period  during  which  the 

planets  were   pulling  the 

sun,  i.e.,  center  of  gravity 

was  in  the  lead 

Dates  when  the 

sun  was  astern 

of  the  center  of 

gravity 

Intervals 
between 

Year 

Intervals 

between 

years 

years 

Year                Year 

1610.8 

1601        to    1608.1 

1605.20 

1619 

8.2 

1614        "    1618.2 

1616.3 

11.05 

1634 

15 

1625       "    1632.5 

1630.35 

14.10 

1645 

11 

1635        "    1643.7 

1639.9 

9.55 

1655 

10 

1649        "    1655.5 

1652.65 

12.75 

1666 

11 

1659.4    "    1668.4 

1663.65 

11 

1679.5 

13.5 

1672.2    "    1677.8 

1673.55 

9.9 

1689.5 

10 

1685       "    1691.3 

1687.9 

14.35 

/^■^^ 

1698X 

9.4 

1696       ''    1701.8 

1698.05 

10.15 

1712 

13.1 

1710       "    1713.3 

1711.76 

13.71 

1723.5 

11.5 

1720       "    1726.5 

1723.28 

11.52 

1734 

10.5 

1733        "    1736.5 

1734.15 

10.87 

1745 

11 

1744        "    1750.4 

1747.8 

13.65 

1755.2 

10.2 

1755       "    1761 

1758.1 

10.3 

1766.5 

11.3 

1769       "    1772.5 

1771.9 

13.8 

1775.5 

9 

1784.7 

9.2 

1779        "    1786 

1783.1 

11.2 

1798.3 

13.6 

1792        "    1796.5 

1794.65 

11.55 

1810.6 

12.3 

1803        "    1811 

1807.8 

13.15 

1823.3 

]2.7 

1812        "    1821 

1817.25 

9.45 

1833.9 

10.6 

1827        "    1833 

1830.2 

12.95 

1843.5 

9.6 

1837        "    1845.8 

1841 . 1 

10.95 

1856 

12.5 

1850.8    "    1855.3 

1851.6 

10.5 

1867.2 

11.2 

1863       "    1869 

1865.95 

14.35 

1878.9 

11.7 

1874       "    1879.5 

1876.15 

10.2 

1890.2 

11.3 

1887.1    "    1891.4 

1890.2 

14.05 

1901.9 

11.7 

1897.5    "    1904.8 

1901.05 

10.85 

20 


TABLE    OF    SUN-SPOT    MAXIMA. 


Sun-spot  Maxima 

(from  Agnes  Gierke's 

History  of  Astronomy) 

Period    during    which    the 
sun  was  pulling  the 

planets,  i.  e.,  sun   was  in 

the  lead  of  center  of 

gravity 

Dates  when  the 
center   of  grav- 
ity   was    astern 
of  the  sun 

Intervals 
between 

"\''po  \* 

Intervals 

between 

years 

years 

1  CTCtl 

Year               Year 

1615.5 

1608.1    to    1614 

1610.8 

1626 

11.5 

1618.2    "    1625 

1621.3 

10.5 

1639.5 

13.5 

1632.5    "    1635 

1632.7 

11.4 

1649 

9.5 

1643.7    "    1649 

1646.45 

13.75 

1660 

11 

1655.5    "    1659.4 

1657.05 

10.6 

1675 

15 

1668.4    "    1672.2 

1671.95 

14.9 

1685 

10 

1677.8    "    1685 

1681.9 

9.95 

1693 

8 

1691.3    "    1696 

1694.1 

12.2 

1705.5 

12.5 

1701.8    "    1710 

1706.3 

12.2 

1718.2 

12.7 

1713.3    "    1720 

1716.2 

9.9 

1727.5 

9.3 

1726.5    "    1733 

1730.2 

14 

1738.7 

11.2 

1736.5    "    1744 

1740.5 

10.3 

1750.3 

n.6 

1750.4    "    1755 

1752.8 

12.3 

1761.5 

11.2 

1761        "    1769 

1765.05 

12.97 

1769.7 

8.2 

1772.5    "    1779 

1774.8 

9.75 

1778.4 

8.7 

1788.1 

9.7 

1786        "    1792 

1788.6 

13.8 

1804.2 

16.1 

1796.5    "    1803 

1799.05 

10.45 

1816.4 

12.2 

1811        "    1812 

1811.65 

12.6 

1829.9 

7.3 

1821        "    1827 

1824.7 

13.05 

1837.2 

12.6 

1833        "    1837 

1835.5 

10.8 

1848.1 

10.9 

1845.8    "    1850.8 

1850.3 

14.8 

1860.1 

12 

1855.3    "    1863 

1859.6 

9.3 

1870.6 

10.5 

1869        "    1874 

1872 

12.4 

1884 

14.4 

1879.5    "    1887.1 

1883.8 

11.8 

1894 

10 

1891.4    "    1897.5 

1894.05 

10.25 

1904.8    " 

1907.86 

13.81 

21 

"While  examining  these  tables  of  sun-spots  maxima  and  minima  it  must 
not  be  forgotten  that  the  original  maker  of  the  tables  given  by  Miss  Gierke — 
Dr.  Rudolf  Wolf — did  not  claim  precision  for  the  dates. 

Professor  Young  says : 

"The  observations  both  of  the  sun-spots  and  of  the  magnetic  elements  near 
the  close  of  the  eighteenth  century  are  so  meager  and  unsatisfactory  that  the 
evidence  as  to  the  precise  time  of  maxima  and  minima  is  very  incomplete. 
It  is  even  doubtful,  as  has  been  said  before,  whether  there  should  not  be 
recognized  an  additional  sun-spot  maximum  in  1795,  over  and  above  those 
enumerated  by  Wolf." — Tlie  Sun,  p.  153. 

Proctor  gives  the  same  table  of  sun-spot  maxima  and  minima  from  1705 
to  1883.8  in  which  the  "possible  error  in  years"  is  given  as  follows:  For 
1705  it  is  two  years;  for  1717.5  and  1727.5  one  year;  for  1738.5  one  and  a 
half  years,  and  for  1750  one  year.    He  says : 

(821)  :  "Professor  Wolf,  in  forming  his  estimate  of  the  mean  period  of 
spot  variation,  endeavored  to  judge,  from  the  imperfect  record  of  sun-spots 
during  the  eighteenth  century,  at  what  times  spots  were  most  or  least 
numerous.  This  part  of  the  evidence  cannot  he  regarded  as  trustworthy. 
Even  if  accepted  as  such,  it  can  he  interpreted  in  more  ways  than  one, 
insomuch  that  epochs  regarded  by  Wolf  as  marked  by  minor  maxima  or 
mimima — the  crests  or  hollows  of  mere  wavelets  of  disturbance  riding  on  the 
main  waves — have  by  others  been  regarded  as  indicating  true  maxima  or 
minima." 

After  giving  the  table  Proctor  proceeds.  (823)  :  "Taking  this  table  as 
it  stands  we  have  fifteen  intervals  from  the  maximum  of  1705.0  to  that  of 
1883.8,  a  range  of  178.8  years,  whence  the  mean  spot  period,  11.92  years, 
would  be  deduced.  The  minima  give  fourteen  intervals  between  1712  and 
1878.5,  a  range  of  166.5  years,  whence  we  get  the  mean  spot  period,  11.89. 
Wolf  estimate  w^as  11.11  years.  It  has  been  suggested  that  a  .small  maxi- 
mum may  have  occurred  in  1797,  which  has  here  been  overlooked;  and  a 
period  of  10.45  years  has  been  inferred.  All  that  can  be  regarded  as  cer- 
tainly established  is  that  the  oscillation  of  spot  frequency  is  irregular,  the 
interval  between  maxima  having  ranged  from  7%  to  15i/'2  years,  and  the 
interval  betweeen  minima  from  9  years  to  13%  years.  No  average  period 
even  can  at  present  he  regarded  as  estahlished ;  and  as  for  the  idea  that  we 
may  find  in  regular  minor  oscillations  some  way  of  making  the  main  oscilla- 
tions appear  regular  (as  being  regularly  modified),  we  may  regard  all 
attempts  in  that  direction  as  not  merely  hopeless,  but  unscientific." — Proctor 
Old  and  New  Astronomy,  348-9. 

Upon  these  and  many  other  like  authorities  I  do  not  think  it  would  be 
profitable  to  discuss  the  many  reasons  why  the  tables  I  give,  based  on 
planetary  motion,  could  be  reconciled  as  to  their  differences  with  Dr.  Wolf's 
tables. 


22 

The  methods  of  observing:  sim  spots  during  the  last  forty  years  have  been 
totally  ehanirod.  Schwab  and  Wolf  merely  counted  the  spots  and  the  days 
of  observation.  Wolf  relied  upon  his  search  in  the  records  of  the  past  as 
to  the  number  of  spots  seen  by  astronomers  who  chanced  to  record  their 
observations. 

With  the  materials  available  to  him  he  worked  wonders  and  it  seems  to 
me  that  had  he  pereisted  in  his  theory  of  planetary  influences,  and  had 
taken  into  account  the  right  planets,  he  would  have  crowned  his  work  with 
a  perfect  theory  fortified  by  laborious  induction. 

The  modern  system  of  obsen'ing  spots  takes  into  account  their  area  and 
the  repetition  of  the  same  spots  also  their  correct  position  on  the  sun  and 
their  time  relations  to  terrestial  phenomena,  besides  preserving  photographs 
of  the  spots. 

The  correspondence  between  the  epochs  of  maxima  and  minima  and  the 
tables  I  have  given,  from  1878.9  to  date,  is  remarkable,  considering  that  the 
movements  of  the  planets  cannot  be  jocke3'ed  nor  the  figures  derivable  there- 
from "coaxed",  to  use  Miss  Gierke's  term,  and  that  the  basis  of  each  set  of 
tables  are  totally  different  in  their  elements. 

But  the  greatest  strain  on  sun  or  planets  by  their  respective  loads  may 
not  always  correspond  to  the  moment  when  that  load  is  directly  astern ;  so 
that  some  variation  may  ultimately  be  made  in  the  tables  on  that  account. 

Returning  now  to  the  plat  of  the  positions  of  the  sun  and  center  of  gravity 
of  the  sj'stem  it  will  be  soon  observed  therefrom  that  marked  periods  occur 
at  lesser,  but  irregular,  intervals,  besides  those  before  given,  on  theory,  from 
the  calculated  positions  of  the  conjunction  of  the  planets,  viz.,  40,  138,  178 
and  218  years. 

Owing  to  the  slow^er  or  faster  motion  of  some  one  of  the  planets  in  arriving 
at  the  conjunction  goal,  the  178  year  period  changes  epoch.  A  more  perfect 
conjunction  occurs  at  a  different  date.  I  find  the  great  year  epochs  change 
according  to  the  following  table,  which  gives  merely  the  date  and  vector 
of  the  center  of  gravity  of  the  system.  Each  column,  it  will  be  seen,  con- 
sists of  dates  a  great  year's  distance  apart,  but  it  will  be  noticed  that  the 
conjunction  w^axes  and  wanes. 


a 


y 


23 


TABLE    OF    EPOCHS    OF   CONJUNCTION    OF    PLANETS. 


B.C. 

B.C. 

B.C. 

917 

925,000 

981 

738 

910,000 

802 

839 

560 

885,000 

623 

660 

380 

890,000 

444 

481 

202 

855,000 

265 

303 

23 

800,000 

83 

905,000 

123 

A.D. 

A.D. 

A.D. 

153 

93 

870,000 

54 

332 

272 

895,000 

233 

810,000 

512 

451 

910,000 

412 

840,000 

690 

630 

920,000 

590 

860,000 

870 

809 

920,000 

770 

870.000 

1048 

988 

930,000 

948 

920,000 

1227 

1167 

910,000 

1127 

930,000 

1406 

1346 

890,000 

1306 

934,000 

1586 

1525 

865,000 

1486 

920,000 

1764 

1704 

835,000 

1665 

905,000 

1883 

810,000 

1844 

880,000 

The  complete  data  for  these  epochs  is  given  in  Table  I,  Appendix. 

From  each  of  these  dates  a  new  set  of  subordinate  periods  will  arise, 
originating  the  great  rollers  and  wavelets,  about  which  Miss  Clerke  and 
Proctor  have  written.  This  table,  with  the  plat  and  Table  III  of  the  appen- 
dix, will  show  how  high  and  in  what  order  these  figurative  waves  are  raised. 
They  will  almost  enable  us  to  measure  the  great  waves  of  convulsed  gases 
which  sweep  around  the  sun  and  dash  into  the  heavens  their  spray  for  hun- 
dreds of  thousands  of  miles. 

We  have  outlined  in  figures  a  condition  from  which  the  reader  can  see 
that  at  times  the  sun  is  towing  its  whole  convoy  of  cruising  planets  through 
the  boundless  ocean  of  space,  now  with  a  very  long  tow  line,  again  with  a 
very  short  one ;  if  we  can  conceive  that  the  vector  length  between  the  sun 's 
center  and  the  center  of  gravity  of  the  system  is  the  tow  line.  Sometimes 
the  sun  tows  a  heavy  load,  sometimes  a  light  load,  as  measured  by  the  dis- 
placement of  the  sun,  which  is  effected  from  time  to  time  by  the  united  or 
separated  attraction  of  the  planets.  This  displacement  varies  from  10,000 
to  934,000  miles. 

At  other  times  the  planets  become  tow  boats  for  the  colossal  battleship, 
towing  him  in  like  manner  as  he  tows  them. 

So  far  we  have  dealt  merely  with  the  coincidence  of  the  dates  of  these 
alternating  results  of  solar  and  planetary  motion  with  the  dates  determined 
from  observations  for  the  solar  disturbances— the  maxima  and  minima  of 


24 

sun  spots.  "We  have  now  to  consider  the  physical  consequences  to  the  sun 
and  planets  of  the  alternating  conditions  of  their  progress  towards  the  apex. 

An  illustration  of  the  nature  of  this  varying  condition  is  hinted  at  by  Sir 
John  Herschel's  comparison,  heretofore  quoted,  which  was  criticised,  as  we 
have  seen  by  Proctor. 

IMost  of  my  readers  are  familiar  with  hammer-throwing  as  a  Held  sport. 
The  "hammer"  is  usually  a  ball  of  lead,  16  pounds  weight,  fastened  to  a 
light  rod  of  iron  as  a  long  handle.  Conceive  the  sun  "leaning  a  little  hack 
as  it  were  to  resist  their  force" — as  Herschel  said.  Conceive  a  hammer- 
thrower  trjdng  to  maintain  a  vertical  and  rigid  position  while  the  hammer 
is  swiftly  circling  about  him  preparatory  to  the  throw.  He  would  be 
speedily  thrown  on  his  face.  The  hammer-thrower  must  lean  back  from  the 
direction  of  the  ball  until  his  pull  equals  the  pull  of  the  ball.  But  let  us 
figure  him  swinging  at  once  four  hammers  of  varying  size,  which,  as  they 
circle  about  him,  separate  at  varying  angles  and,  now  and  then,  join  on 
one  line  and  exert  all  their  pull  in  one  direction.  The  hammer-thrower 
will  be  in  alternating  conditions  of  stress ;  now  he  is  pulled  one  way  hy  the 
united  force,  again  the  pull  comes  from  four  directions  at  once,  each  ham- 
mer's pull  neutralizing  the  pull  of  another.  Again  let  us  imagine  him 
moving  rapidly — say  on  roller  skates,  and,  thus  moving,  swinging  his  ham- 
mers, and  we  w411  have  a  varying  condition  of  strain  in  all  directions,  now 
urging  him  forward,  again  sideways,  or  even  arresting  his  progress,  as  the 
motion  of  the  hammers  in  their  circuits  may  cause. 

Such  is  the  condition  of  the  sun.  As  it  glides  through  space  to  its  apex 
it  is  urged  sideways,  backwards  or  forwards  with  an  energy  immeasurably 
greater  than  our  conceptions  of  horsepower  or  kilowatts  can  express.  It 
is  subject  to  a  constant  and  variable  physical  stress  from  without  that  must 
act  upon  its  mobile  mass  as  a  shaking  grate  acts  upon  a  boiler  fire. 

Sir  R.  S.  Ball  says : 

"There  are  no  absolutely  rigid  bodies  known  in  nature,  for  the  hardest 
mineral  or  toughest  steel  must  yield  to  some  extent  when  large  forces  are 
applied  to  it,  and  as  the  bodies  in  the  system  are  not  mere  points  or  par- 
ticles of  inconsiderable  dimensions  they  will  experience  stresses  something 
like  those  to  which  our  earth  is  subjected  in  that  action  of  the  moon  and 
sun  which  produces  the  tides.  In  consequence  of  the  influences  of  each  body 
on  the  rest,  there  will  be  certain  relative  changes  in  tlie  parts  of  each  body; 
there  will  be  as  it  were  tidal  movements  in  their  li(iuid  parts,  and  even  in 
their  solid  substance." — The  Earth's  Beginning,  p.  219;  also  ^VinchclVs 
^Yorld  Life,  2d  Ed.  1883,  pp.  222,  et  seq. 

The  strength  of  the  gravitational  force  binding  the  earth  to  the  sun  has 
been  likened  to  that  of  innumerable  steel  telegraph  wires  set  as  thickly  in 
the  earth  as  blades  of  grass.  Let  us  imagine  that  such  l)onds  of  force — 
invisible — envelop  like  a  net  Jupiter  and  the  sun  and   control  in  their 


25 

meshes  every  particle  of  the  solid  and  gaseous  materials  of  those  bodies,  the 
strands  between  forming  rigid  cables  uniting  the  bodies.     When  by  their 
motions- — Jupiter  circling  about  the  sun,  the  sun  rushing  towards  its  apex — 
those  bodies  change  their  relative  positions  one  to  the  other,  there  will  result 
a  drawing  of  these  nets  and  a  compression  of  the  enclosed  spheres  changing 
their  forms  to  pear-shaped  spheroids  with  their  smaller  ends  pointed  towards      ? 
each  other;  a  tide  of  matter  will  be  literally  squeezed  out  on  that  side  of      y 
each  globe  nearest  to  the  other  and  will  course  around  each  sphere  as  each      ?• 
body  rotates  upon  its  axis.  j 

So  if  all  four  of  the  great  planets  are  so  bound,  pulling  upon  their  net-like 
bonds  a  bulging  of  the  mass  of  the  sun  and  a  squeezing  of  its  material 
towards  the  opposing  planets  must  result.  At  the  moment  when  all  four 
are  in  one  line  on  one  side  of  the  sun  compression  will  be  exerted  to  the 
uttermost  upon  the  elastic  gases  of  the  sun  as  if  it  were  in  the  socket  of  a  ball 
and  socket  joint  when  the  screw  was  being  tightened.  At  these  times  motion 
is  compelled  in  the  sun's  mass  towards  the  planets ;  and,  upon  those  parts  of 
the  sun  which  are  denuded  of  such  tide-forming  material,  outbreaks  of  the 
submerged  matter  and  guess — relieved  temporarily  of  super-incvimbent 
weight — wall  occur  as  a  result  of  their  expansion,  which  may  be  so  violent  as 
to  constitute  an  explosion. 

Now  reverse  the  order  of  the  procession,  putting  the  planets  in  the  lead 
moving  towards  the  apex,  then  the  pull  upon  the  sun's  mass  will,  to  that 
extent,  be  relaxed.  Then  the  compressed  gases  of  the  sun  will  expand  and 
will  be  redistributed  by  gravitation  about  the  sun,  and  it  will  regain  its 
speroidal  form.  Thus  the  sun  will  have  alternating  periods  of  compression 
and  expansion  of  varying  degrees  of  intensity  proportional  to  the  amount 
and  direction  of  the  attractive  forces  of  the  planets  and  the  degree  of 
unity  or  diversity  in  their  action. 

Now  let  us  see  how  far  observation  tends  to  support  these  suggestions.  We 
need  merely  mention  the  fact  that  Helmholtz  propounded  the  generally 
accepted  theory  of  the  gravitational  shrinkage  of  the  sun  as  the  cause  of 
its  heat;  and  that  Sir  Wm,  Herschel,  Arago  and  others  have  traced  an 
annual  variability  in  the  quantity  of  heat  by  the  variable  crops  and  their 
prices,  corresponding  to  sun-spots  periods. 

In  1884  Dr.  J.  Helfiker  published  a  pamphlet  in  which  he  discussed  the 
variability  of  the  solar  diameter,  using  3,468  transits  of  the  sun  observed 
during  22  years  at  the  Neuchatel  Observatory  and  found  that  such  changes 
in  the  diameter  of  the  sun  bore  a  relation  to  the  period  of  the  sun-spots ; 
that  is  to  say,  that  the  greatest  diameter  coincided  with  the  minimum 
of  the  period  of  sun-spots  and  vice  versa. — Observatory  for  Sept.  1884,  p. 
263;  T.  Ililfiker,  Premiere  etude  sur  Ics  ohservations  du  diametre  du  Soliel. 
Bulletin  de  la  Societe  des  Sciences  Naturelle,  Neuchatel  Tome.  XIV. 


/ 


\ 


( 


26 

Professor  Charles  Lane  Poor,  in  June,  1905,  published  an  article  on  the 
"Figure  of  the  Sun",  giving  photographic  evidence  "that  the  ratio  between 
the  polar  and  equatorial  radii  of  the  sun  is  variable,  and  that  the  period  of 
this  variability  is  the  same  as  the  sun-spot  period."  He  says:  "The  sun 
appears  to  be  a  vibrating  body  whose  equatorial  diameter  on  the  average 
exceeds  the  polar  diameter.  At  times,  however,  the  polar  diameter  becomes 
equal  to  and  even  greater  than  the  equatorial — the  sun  passing  from  an 
oblate  to  a  prolate  spheroid.  In  this  variable  figure  may  be  the  explana- 
tion of  the  anomalies  in  the  motions  of  Mercury,  Venus  and  Mars." — Astro- 
physkal  Journal,  Vol.  22,  p.  113. 

"]\Ieasurements  made  by  the  same  person,  however,  and  with  the  same 
instruments,  but  at  different  times,  sometimes  differ  enough  to  raise  a  suspi- 
cion that  the  diameter  is  slightly  variable,  which  would  be  nothing  surpris- 
ing, considering  the  nature  of  the  solar  surface. — Young,  "Sun,"  p.  45,  Ed. 
1881. 

In  the  facts  and  events  suggested  by  this  chapter  we  have  a  sufficient 
cause  for  the  shrinkage  and  expansion  of  the  sun  which  fits  all  of  the 
observations  and  theories  of  solar  activity,  both  as  to  the  time  of  their 
occurrence  and  as  to  the  variable  intensity  of  their  action. 

We  may  summarize  as  follows : 

There  is  a  disturbance  of  the  sun 's  mass  and  motion  by  the  planets  which 
is  sufficient  at  times  to  drive  the  whole  mass  of  the  sun  aside  from  its 
path  to  the  extent  of  twice  the  diameter  of  the  moon 's  orbit.  Such  a  force, 
acting  upon  a  body  of  elastic  gas,  must  raise  what — for  want  of  a  better 
name — we  must  call  a  tide  or  tides  of  great  height.  The  flow  of  these  tides 
relieves  the  pressure  upon  portions  of  the  sun,  allowing  submerged  gases — 
too  heavy  to  be  ordinarily  exposed — to  manifest  their  existence  by  ebullition 
and  explosion,  giving  rise  to  phenomena  only  periodically  displayed. 

The  tables  show  that  the  energy  of  the  planets  is  maintained  almost  con- 
stantly upon  the  sun's  motion.  It  is  very  frequently  sufficient  to  drive  the 
sun  aside  from  its  path  600,000  miles ;  still  more  frequently  200,000  miles ; 
the  exceptions  to  the  latter  force  being  as  infrequent  as  to  the  exertion  of 
the  greatest  force — viz.,  that  exceeding  600,000  miles. 

It  is  therefore  probable  that  this  merely  physical  disturbance  of  the  sun's 
mass — this  constant  and  variable  raking  of  the  solar  fires — gives  rise  to  all 
of  the  effects  known  as  spots,  prominences,  coronas,  magnetic  storms  and 
other  phenomena  of  solar  activity. 


27 


EARTHQUAKES    WHICH    ARE    PROBABLY   CAUSED    BY 
SOLAR   AND    PLANETARY   ACTION. 

The  theory  of  the  generation  of  the  moon,  propounded  by  Professor 
G.  H.  Darwin — see  his  work  on  "Tides" — outlines  the  first  case  of  solar 
action  producing  an  earthquake,  for  which  we  have  his  mathematical 
authority.  As  such  it  antedates  all  geological  records  displayed  to  us  in 
faults,  fissures,  mountains  and  volcanoes.  Prof.  Wm.  II.  Pickering,  in  an 
article  published  in  Harper's  Magazine  for  June,  1907,  briefly  outlines  this 
theory  of  the  moon's  generation. 

Not  all  earthquakes  are  the  result  of  solar  action.  An  earthquake  is  a 
shaking  of  the  earth's  crust.  A  shock  produced  by  the  explosion  of  a 
giant  powder  factory  will  give  the  same  effects  as  a  slight  earthquake.  Some 
earthquakes  are  directly  traceable  to  explosions  of  steam  and  some  to  explo- 
sions of  other  gases. 

Some  are  indeterminate,  perhaps  partly  terrestrial  and  partly  solar  in 
origin. 

Prof.  G.  H.  Darwnn  says : 

"Earthquakes  are  probably  due  to  unequal  shrinkage  of  the  planet  in 
cooling,  and  each  shock  would  tend  to  bring  the  strata  into  their  position  of 
rest ;  thus  the  earth 's  surface  would  avail  itself  of  the  opportunity  afforded 
by  earthquakes  of  acquiring  its  proper  shape." — Darwin's  Tides,  p.  300-1. 

Both  Darwin  and  Sir  R.  S.  Ball  unite  substantially  in  the  following 
opinion : 

"The  attractions  of  the  moon  and  sun  must  certainly  act  not  only  on  the 
sea,  but  also  on  the  solid  earth ;  and,  since  the  earth  is  not  perfectly  rigid 
or  stiff,  they  must  produce  an  alternating  change  in  its  shape.  Even  if  the 
earth  is  now  so  stiff  that  the  changes  in  its  shape  escape  detection  through 
their  minuteness,  yet  such  changes  of  shape  must  exist." — Darwin's  Tides, 
p.  3;  Ball,  The  Earth's  Beginning,  pp.  163, 164, 168,  176. 

At  certain  periods  of  the  progress  of  the  solar  system  during  the  past  28 
centuries  violent  earthquakes  have  occurred.  Our  information  is  for  the 
most  part  confined  to  those  occurring  in  Europe  or  around  the  Mediter- 
ranean Sea.  After  the  beginning  of  the  16th  century,  A.  D.,  America  was 
included  in  the  catalogue.  Such  early  Chinese  and  Japanese  records  as  are 
available  strengthen  the  inferences  to  be  drawn  herein  from  the  European 
records. 

As  to  the  \QTy  early  records  it  may  be  safely  asserted  that  only  those 
records  of  earthquakes  of  great  and  widespread  intensity  have  been  handed 
down,  because  early  civilization  and  reliable  history  centers  about  the 
Mediterranean  Sea,  which  has  always  been  earthquake  territory.     Conse- 


28 

qiiently  a  commonplace,  ordinary  (juake  would  pass  nnnotieod,  and,  in  most 
instances,  the  early  records  manifestly  deal  with  grreat  eartlKpiakes  only. 

The  few  instances  of  Chinese  and  Japanese  ancient  records  also  deal  w  itli 
world-shakin*;  events. 

The  epochs  when  all  tlie  great  planets  were  in  conjnnction,  as  shown  by 
Table  I,  appendix,  have  been  historically  marked  by  world-shaking  quakes 
in  almost  every  instance,  as  will  be  seen  from  an  examination  of  IMallett's 
"Earth(iuake  Catalogue"  R.  and  F.  W.  ]\Iallet  1858. 

The  dates  when  the  sun  is  crossing  the  line  of  the  center  of  gravity,  as 
shown  l)y  Table  III,  either,  while  in  tow  of,  or  while  being  towed  by  the 
planets,  are  also  the  dates  of  many  great  earthquakes. 

The  periods  during  which  the  sun  makes  its  widest  departures,  East  or 
West,  of  the  path  of  the  center  of  gravity,  namely  in  excess  of  500,000 
miles,  are  also  periods  when  many  of  our  great  quakes  happen. 

The  same  effects  must  be  produced  upon  each  planet  by  the  alternating 
conditions  of  progress,  as  are  visibly  produced  upon  the  sun  when  it  varies 
from  maxima  to  minima  of  violent  disturbance,  that  is,  great  commotion 
and  movement  in  its  fluid  or  gaseous,  or  even  solid  materials,  and  shrinkage 
or  expansion  around  the  equatorial  zone. 

Whether  this  shrinkage  or  expansion  can  be  measured  depends  on  the 
condition  of  the  planet.  A  movement  of  the  crust  of  the  earth,  horizontally 
or  vertically,  for  10  or  20  feet  will  not  represent,  as  to  the  whole  globe, 
much  of  a  shrinkage  or  expansion,  but  it  may  result  in  the  ruin  of  a  city 
or  a  state.  To  the  extent  that  the  earth  is  mobile  and  plastic  enough  to 
respond  to  the  stress  put  upon  it  during  seasons  of  great  stress,  to  that 
extent  should  its  crust  yield  to  the  shrinkage  or  expansion  of  its  interior. 
Even  cold  steel  and  iron  can  be  made  to  yield  and  change  form  under  cold 
pressure  in  the  mechanic  arts,  not  alone  in  minute,  but  in  great  masses. 
The  idea  that  the  earth  is  rigid  or  stiff  enough,  therefore,  to  resist  the 
almost  immeasurable  stresses  put  upon  it  by  the  solar  system  can  have  no 
foundation.  If  great  cataclysms  in  the  past  have  rent  it  through  and 
through,  establishing  fissures  deeply  and  extensively  across  the  earth  it 
would  be  reasonable  to  expect  that,  when  the  strain  was  again  felt,  the 
earth  would  again  yield  practically  along  -the  same  lines,  reopening  the 
same  Assures.  Observation  in  mines  and  elsewhere  shows  such  repeated 
breaks.  Periodical  recurrence  of  earthquakes  along  the  same  line,  which 
are  not  accompanied  by  evidence  of  explosive  force,  or  of  falling,  and 
which  affect,  during  short  intervals,  the  whole  sphere  along  a  great  circle, 
and  which  occur  uniformly  with  certain  conditions  of  the  progress  of  the 
solar  system,  point  to  a  causal  relation  of  the  two  conditions. 

The  visible  condition  of  the  moon  is  that  it  is  a  wreck  of  moon  quake 
activities,  seamed  with  fissiires,  honeycombed  with  volcanoes  and  wrinkled 
with  mountain  chains,  the  product  of  shrinkage. 


29 

The  visible  condition  of  the  sun  is  an  almost  ''continuous  performance" 
of  sun  quake,  varying  in  intensity,  as  we  have  seen. 

The  condition  of  the  other  planets  seems  to  be  the  same  so  far  as  observa- 
tion can  determine. 

Referring  to  Tables  I  and  II,  the  reader  will  see  that  the  year  1804  was  a 
conjunction  epoch,  the  four  great  planets  being  nearly  in  line,  Saturn 
lagging  back. 

August  5th,  1803,  Schroter  found  Saturn  not  perfectly  spheroidal  in 
figure.  In  April  and  May,  1805,  Sir  Wm.  Herschel,  after  most  careful 
observations  to  exclude  all  instrumental  or  other  errors,  found  that  Saturn 
"resembles  a  parallelogram,  one  side  whereof  is  parallel  to  the  equatorial, 
the  other  to  the  polar  diameter,  with  the  four  corners  rounded  off  so  as  to 
leave  both  the  equatorial  and  the  polar  regions  flatter  than  they  would  be 
in  a  regular  spheroidal  figure."  He  renewed  these  observations  in  1806 
v/ith  the  same  result.  But  he  found  that  in  1807  a  change  had  taken  place 
in  the  aspect  of  the  planet.  In  1818  Kitchener  saw  the  same  figure.  The 
changing  form  of  the  planet  has  been  often  noticed. 

Proctor  concludes:  "We  seem  almost  compelled,  therefore,  to  accept 
the  conclusion  that  the  planet  Saturn  is  subject  to  the  influence  of  forces 
which  either  upheave  portions  of  its  surface  from  time  to  time,  or  cause 
vast  masses  of  cloud  to  rise  to  an  enormous  height  above  the  mean  level  of 
Saturn's  cloud  envelope.  *  *  *  which — to  be  discernable  from  our  dis- 
tant standpoint — would  imply  the  expansion  and  contraction  of  whole 
zones  of  Saturn's  surface  through  4,000  or  5,000  miles  at  least." — Proc- 
tors Familiar  Science  Studies,  p.  61;  Proctor's  Other  Worlds  Than  Ours, 
Saturn;  Proctor's  Astronomical  Essays,  101;  Arago  Pop.  Ast.,  Vol.  2,  p.  599. 

Jupiter  also  exhibits  these  changes  of  form. 

Proctor  says : 

"We  have  seen,  however,  that  evidence  is  not  wanting  to  prove  that 
Jupiter  is  really  liable  to  occasional  changes  of  figure,  though  not  to  such 
an  extent  as  to  change  the  general  aspect  of  the  planet." — Other  Worlds 
Than  Ours,  pp.  151,  157,  173;  Familiar  Science  Studies,  pp.  60,  75;  Arago 
Pop.  Ast.,  Vol.  2,  p.  521. 

The  "canals"  of  Mars  may  be,  in  part  at  least,  immense  fissures.  There 
is  no  reason  apparent  why  any  planet  should  differ  from  another  in  being 
subject  to  such  planet  quakes. 

Another  form  of  force  is  manifested  by  the  sun  as  a  product  of  its  com- 
motions, different  from  the  merely  mechanical  energy  of  its  moving  mass. 
The  electrical  effects  upon  the  earth,  which  have  been  traced  to  the  sun  as  a 
cause,  are  as  closely  connected  with  its  variable  condition  as  are  its  spots. 
Such  effects  as  "magnetic  storms"  have  been  connected  with  particular 
meridians  and  latitudes  of  the  sun.  A  "storm"  having  been  observed  to 
originate  when  a  particular  spot  appeared,  a  repetition  of  the  storm  has 


30 

been  observed  when  tbe  synodical  rotation  of  that  part  of  the  sun  had  again 
brought  it  to  bear  upon  the  earth.  But  as  the  rotation  speed  of  the  sun 
varies  the  repetition  of  the  phenomena  will  occur  at  a  longer  or  shorter 
interval.  The  sidereal  rotation  of  the  sun  at  the  equator  requires  25  days 
41  o  hours,  while  at  North  latitude  50°  and  South  latitude  45°  it  requires 
27  days  IO34  hours.  We  must  add  2  days  to  the  sidereal  time  in  order  to 
get  the  synodical  time  of  rotation,  so  that  some  latitudes  of  the  sun  require 
the  same  length  of  time  to  complete  a  revolution,  respecting  the  earth,  as 
does  the  moon.  Thus,  for  those  latitudes  of  the  sun,  the  moon  becomes  a 
clock  Avith  which  to  time  the  rotation  of  those  portions  of  the  sun ;  and,  as 
such  portions  are  very  active,  we  may  have  here  the  reason  for  the  popular 
belief  in  the  moon  as  a  cause  of  many  terrestrial  phenomena  which  in  fact 
have  their  origin  in  the  sun,  eartlKpiakes  among  the  number. 

Pcrrey's  catalogues  of  earthquakes  and  his  efforts  to  connect  the  phases 
of  the  moon  therewith  may  have  great  value  when  examined  from  the  view 
of  the  sun  being  the  cause. 

In  an  article  published  in  Harper's  Magazine  for  May,  1905,  "Magnetic 
Storms  and  the  Sun",  Professor  ^Maunder  says  that  he  noticed  that  when 
certain  great  sun-spots  reached  the  center  of  the  sun's  disc  a  great  magnetic 
storm  broke  out  on  the  earth,  accompanied  in  one  instance  by  a  most  re- 
markable aurora.  He  says  that  he  "noticed  four  disturbances  toward  the 
end  of  the  year  1886  and  four  in  the  middle  of  the  following  year,  which 
succeeded  each  other  at  almost  equal  intervals  of  time ;  the  intervals  being, 
on  the  average,  about  twenty-seven  days  eight  hours — just  the  interval 
which  it  takes,  on  the  average,  for  a  sun-spot  to  pass  from  the  center  of  the 
sun's  disc  round  to  that  center  a  second  time." 

From  this  article  it  would  seem  as  if  great  electrical  guns  were  mounted 
upon  the  sun  which  now  and  then,  loaded  by  its  energy  and,  getting  our 
range  as  they  s\Aing  round,  give  us  a  shot  to  emphasize  our  mortality.  These 
electrical  discharges  may  prove  to  be  of  many  kinds  and  from  different 
latitudes  of  the  sun. 

I  refer  again  to  the  long  list  of  earthquakes  extending  over  a  great  period 
of  time  catalogued  by  Mallet,  which  were  accompanied  by  auroras,  loud 
detonations,  electrical  storms  and  other  electrical  phenomena  of  a  most 
extraordinary  character.  It  is  also  to  be  remarked  that  extraordinary 
alternations  of  heat  and  cold,  wind  and  rain,  storms  of  great  violence,  mark 
earth(|uake  years,  as  evidenced  hy  that  catalogue  and  by  the  years  1906 
and  1907. 

It  is  also  to  be  noticed  that  the  time  within  which  magnetic  or  electrical 
forces  reach  the  earth  after  starting  from  the  sun  is  in  doubt,  it  appearing 
that  some  forms  of  this  force  are  instantaneous,  quicker  than  light,  while 
other  forms  are  very  slow  comparatively.     Ricco  and  Arrenhius  calculate 


31 

45  hours  as  the  time  required  for  electrical  force  to  reach  the  earth  from 
the  sun.— Set.  Am.  Supi).  July  15th,  W05,  p.  20,698. 

But,  in  the  article  already  quoted,  Prof.  ]\Iaunder  makes  the  suggestion 
that  when  the  magnetic  or  electrical  streams  proceeding  from  the  sun  hap- 
pen to  intersect  the  earth  they  cause  a  release  of  energy  in  the  electrical 
forces  of  the  earth  "  as  a  spark  may  set  free  the  disruptive  forces  in  a  store 
of  gunpowder.  The  solar  action  Avill  be  indeed  the  cause  of  the  storm,  but 
it  will  be  so,  not  as  supplying  the  forces  put  forth  in  it,  but  as  giving  them 
the  opportunity  to  reveal  themselves. ' ' 


32 


A    PRELIMINARY   CHAPTER    ON    SOLAR    AND 
PLANETARY    MOTION. 

The  object  of  this  chapter  is  to  briefly  state  some  facts,  in  a  new  relation, 
which  tend  to  show  that  the  sun's  motion  towards  the  sohir  apex  has  a 
critical  speed  which  it  must  maintain  in  order  to  furnish  planetary  paths 
conformable  to  observation,  and  that  such  speed  exceeds  that  given  by 
some  authorities  and  need  not  be  as  great  as  allowed  by  others.  The  most 
recent  authorities  are  very  conservative,  but  as  their  observations  govern 
their  results  it  cannot  be  said  that  any  bias  exists  in  favor  of  a  great  or  a 
slow  speed.  They  give  a  speed  of  about  12  miles  a  second.  ]\Iiss  Gierke, 
however,  exhibited  the  natural  bias  of  an  elderly  lady  in  saying:  "We  are 
not  whirled  in  the  train  of  such  a  stellar  projectile  as  1830  Groombridge. " 

There  is  another  purpose  in  this  chapter,  which  is  to  secure  attention 
to  the  true  motion  of  the  solar  system,  which  is  certainly  quite  different  from 
that  set  forth  by  Gopernicus  or  Kepler,  but  which,  nevertheless,  still  con- 
forms to  the  mathematical  relations  stated  by  Kepler  and  Newton  when 
proper  allowance  is  made  for  the  solar  and  planetary  motion  towards  the 
solar  apex. 

In  1890  IMiss  Gierke  summed  up  the  conclusions  of  astronomers  as  to  the 
direction  of  the  sun's  motion  by  placing  the  apex  in  R.  A.  273°  21',  north 
declination  27°  19';  and  gave  the  speed  at  14i/o  miles  per  second — History 
of  Astronomy,  pp.  324,  325,  3rd  Ed. 

Again  she  said: 

"But  when  from  the  direction  we  attempt  to  pass  to  the  amount  of  solar 
motion,  the  case  becomes  widely  ditt'erent.  Flagrant  contradictions  abound. 
Estimates  of  velocity  range  at  large  between  five  and  150  miles  a  second; 
the  criteria  of  truth  are  at  the  mercy  of  individual  judgment.  The  cause 
of  these  discrepancies  lies  in  the  uncertainty  still  prevailing  as  to  the  dis- 
tances of  the  stars.     *     *     * 

"It  is  nevertheless  tolerably  certain  that  the  solar  pace  has  nothing 
headlong  about  it.  We  are  not  whirled  in  the  train  of  such  a  stellar  pro- 
jectile as  1830  Groombridge  or  Zeta  Toucani.  Our  condition  were  it  so 
would  be  betrayed  by  unmistakable  tokens.  Everything,  on  the  contrary, 
suggests  the  inference  that  our  sun  is  among  the  sedately  moving  stars." — 
System  of  the  Stars,  p.  326,  Agnes  M.  Gierke,  Oct.,  1890. 

Again  she  says : 

"We  do  not  know  the  plane  of  the  sun's  orbit — only  the  direction  of  one 
line  in  it,  and  that  line,  pointing  towards  the  constellation  Hercules,  makes 
an  angle  of  about  60°  with  the  sun's  equator.  Tims,  the  solar  movements 
of  rotation  and  translation  would  seem  to  he  unrelated  one  to  the  other; 


33 

and  the  same  remark  applies  to  the  planetary  revolutions  conducted,  on  the 
whole,  along  levels  of  space  differing  very  little  from  that  of  the  great 
globe's  axial  movement.  Our  whole  system  is  then  driven  obliquely  upward 
by  a  power  which,  taking  no  apparent  account  of  its  domestic  economy 
owned  doubtless  an  origin  totally  disconnected  from  that  of  gyrations  given, 
through  it  influence,  the  helicoidal  shape  illustrated  in  Fig.  48."  (Here 
follows  a  figure  showing  the  sun's  way  directed  upward  at  an  angle  of  55° 
from  an  ellipse  to  represent  perhaps  the  principal  plane  of  the  solar  system, 
and  about  it  the  path  of  the  earth  consisting  of  a  long  arc  followed  by  a 
small  loop  similar  to  figure  3  herein.) — Gierke,  System  of  the  Stars,  p.  330. 

The  speed  of  14.5  miles  per  second  equals  460  million  miles  per  annum. 

Sir  John  Ilerschel  rates  the  speed  of  the  sun  at  154  million  miles  per 
annum,  or  nearly  5  miles  a  second,  very  much  the  slowest  of  any  speed 
assigned. — Outlines  of  Astronomy,  Art.  858. 

Prof.  Newcomb,  in  ''The  Stars",  published  in  1902,  cites  many  authori- 
ties giving  different  directions  and  speeds  and  sums  up  as  follows : 

"From  all  these  results  it  would  seem  that  the  most  likely  apex  of  the 
solar  motion  is  towards  a  point  in  Right  Ascension  280°,  Declination  30° 
North.  This  point  is  situated  in  the  constellation  Lyra  about  4°  from  the 
first  magnitude  star,  Vega. — Tlie  Stars,  Newcomh,  p.  91. 

At  page  93  he  gives  a  speed  of  19  kilometers  per  second,  or  11.8  miles,  or 
372  million  miles  per  year. 

Maedler  estimated  the  sun's  motion  towards  the  apex  at  30  miles  per 
second,  or  946,728,000  miles  yearly. — Gierke's  Hist,  of  Ast.,  49.  -^  -, 

And  Rancken  estimated  it  at  9.79  times  the  radii  of  the  earth's  orbit.—  y^  ^1  ^FC 
Phil.  Soc.  Wash.,  Vol.  XI,  pp.  143,  17 1  c?  - 

Rancken 's  estimate  is  over  907  million  miles  yearly — about  28  miles  a    /      7f  ,    /^ 

second. 

Miss  Gierke  does  not  cite  the  authorities  who  assign  a  velocity  up  to  150 
miles  a  second. 

As  a  result  we  find  professional  astronomers  estimating  the  sun's  motion 
through  space  at  a  speed  of  from  five  to  150  miles  a  second,  with  a  direction 
that  varies  in  longitude  from  260°  to  289°,  and  in  declination  from  +14° 
to  +53°.  Professor  W.  W.  Campbell,  the  latest  cited,  places  the  declination 
at  +20°. 

In  ordinary  terms  the  sun's  path  is  in  a  plane  inclined  to  the  ecliptic 
and  to  the  principal  plane  of  the  solar  system  and  the  angle  of  inclination 
is  in  dispute  to  the  extent  of  40°. 

The  speed  and  the  angle  of  inclination  of  the  sun's  path  to  the  principal 
plane  of  the  solar  system  are  of  most  consequence  in  this  chapter. 

By  reference  to  many  books  it  will  be  seen  that  the  sun's  path  through 
space  is  depicted  like  that  of  a  rocket  rising  into  the  heavens  from  a  field 
bounded  by  an  ellipse  to  represent  the  principal  plane  of  the  solar  system, 


34 

while  the  earth  is  shown  winding  upwards  and  around  the  sun's  path  in  an 
ascending:  spiral,  like  a  ball  under  the  feet  of  a  performer  in  a  circus. 

See  Miss  Gierke's  "System  of  the  Stars",  p.  330. 

Variety  is  given  to  this  by  Flammarion;  he  shows  the  same  spiral,  but 
descending,  "falling"  literally,  he  says.     (Pop.  Ast.,  p.  52.) 

Still  more  elaborate  is  an  illustration  in  Gillet  and  Rolfe's  Astronomy, 
p.  369,  showing  the  spiral  paths  of  all  the  planets  with  earth  and  moon 
prominently  wiggling  their  compound  way  "up  dem  golden  stairs." 

According  to  these  illustrations,  the  solar  system  follows  an  inclined 
cylindrical  path  upwards  at  an  angle  of  about  55°  from  the  plane  of  revolu- 
tion of  the  solar  system,  in  which  plane  the  horizontal  trace  of  the  spiral 
path  of  each  planet  forms  a  closed  ellipse. 

This,  of  course,  is  very  foreign  to  the  Copernican  system.  But  the  sta- 
tionary sun  called  for  by  that  system  is  now  replaced  by  a  body  which,  as 
we  have  seen,  is  said  to  move  at  a  velocity'  somewhere  between  5  and  150 
miles  per  second,  and  it  is  felt  that  something  must  be  said  to  reconcile  the 
two  repugnant  ideas — namely  revolutions  of  the  planets,  in  closed  ellipses 
with  a  swiftly  moving  body  around  which  such  revolutions  take  place. 

Miss  Gierke  says:  "We  do  not  know  the  plane  of  the  sun's  orbit — only 
the  direction  of  one  line  in  it."  That  was  an  oversight,  because  the  fact 
that  the  sun  makes  an  irregular  cycloidal  revolution  about  the  center  of 
gravity  of  the  system  was  no  doubt  well  known  to  her.  As  we  have  already 
seen  this  orbit  may  extend  at  times  934,000  miles  or  more  to  one  side  of 
that  center.  So  we  have  a  plane  nearly  two  million  miles  across,  with 
a  line  in  that  plane  formed  by  the  motion  of  the  center  of  gravity.  There- 
fore, we  have  a  plane  nearly  2  million  miles  wide  and  infinitely  long, 
extending  in  the  general  direction  from  90°  to  270°  heliocentric  longitude, 
in  which  the  sun  moves.  The  plane  of  the  sun's  motion  by  virtue  of  the 
sun 's  mass  is  approximately  the  principal  plane  of  the  solar  system. — Ball 's 
Earth's  Beginning,  pp.  208,  210. 

But  all  the  motions  of  the  great  planets  take  place  within  two  planes 
very  closely  parallel  to  the  principal  plane  according  to  ohscrvation,  whether 
such  motion  is  in  closed  ellipses,  epicycles,  spirals,  serpentine  or  other 
curved  paths. 

The  proposition  involved  is  whether  planetary  motion  through  space 
with  the  sun,  and  as  viewed  from  the  stars,  is  cylindrical  and  spiral  or 
whether  it  is  essentially  confined  to  a  plane  (using  that  term  here  to  signify 
a  fiat  space  confined  within  two  planes)  and  the  planetary  motions  are  in 
open  or  closed  curves. 

Is  the  principal  plane  of  the  solar  system  like  the  floor  of  an  elevator 
moving  up  or  down  a  shaft? 

With  reference  to  the  walls  of  the  shaft,  does  the  astronomer  see  the 
bricks  of  the  shaft  moving  up  or  down  in  lines  perpendicular  to  the  floor 


35 

of  the  elevator,  or,  in  lines  oblique  to  that  floor?  If  he  sees  the  stars  moving 
in  lines  very  oblique  to  the  principal  plane  of  the  system  then  the  spiral 
paths  of  the  planets — if  they  are  spiral — will  be  very  flat  and  maj^  be  fairly 
represented  by  their  horizontal  trace  in  the  plane  of  the  solar  system. 

But  under  any  of  the  modern  theories  of  this  motion — as  to  direction 
and  speed — it  is  evident  that  the  path  of  a  planet  cannot  be  a  closed  ellipse 
unless  the  solar  apex  lies  in  a  line  perpendicular  to  the  principal  plane  of 
the  solar  system. 

The  motions  of  the  moon  have  been  more  closely  studied  than  those  of 
any  other  body.  The  papers  and  books  of  Prof.  G.  H.  Darwin  have  pre- 
sented them  again  in  a  new  way.  In  his  papers  and  books  on  tidal  forces 
he  traces  mathematically  the  history  of  the  earth  and  moon  "until  the 
moon  nearly  touches  the  earth,  and  the  two  go  round  each  other  like  a  single 
solid  body  in  about  three  to  five  hours." — Tides,  p.  278.  *  *  *  "It  is 
by  methods  of  rigorous  argument  that  the  moon  is  traced  back  to  the  initial 
unstable  condition  when  she  revolved  close  to  the  earth.  But  the  argument 
here  breaks  down,  and  calculation  is  incompetent  to  tell  us  what  occurred 
before,  and  how  she  attained  that  unstable  mode  of  motion. — Tides,  p.  281. 
************ 

"We  have  grounds  for  conjecturing  that  the  moon  is  composed  of  frag- 
ments of  the  primitive  planet  which  we  now  call  the  earth,  which  detached 
themselves  when  the  planet  spun  very  swiftly,  and  afterwards  became 
consolidated. ' ' — Same,  p.  282. 

lie  then  mathematically  traces  the  history  of  earth  and  moon  forward, 
saying : 

"The  moon  must  then  always  face  the  same  part  of  the  earth's  surface, 
and  the  two  bodies  must  move  as  though  they  were  united  with  a  bar.  The 
outcome  of  the  lunar  tidal  friction  will  therefore  be  that  the  moon  and 
the  earth  go  round  as  though  locked  together  in  a  period  of  fifty-five  of  our 
present  days,  with  the  day  and  the  month  of  identical  length." — p.  276. 
************ 

"The  series  of  changes  then  proceed  until  the  two  periods  come  again 
to  an  identity,  when  we  have  the  earth  and  the  moon  as  they  were  at  the 
beginning,  revolving  in  the  same  period,  with  the  moon  always  facing  the 
same  side  of  the  earth.  But  in  her  final  condition  the  moon  will  be  a  long 
way  off  the  earth,  instead  of  being  quite  close  to  it. ' ' — p.  280. 

"When  there  is  only  one  day  in  the  month,  the  earth  and  the  moon 
go  round  at  the  same  rate,  so  that  the  moon  always  looks  at  the  same  side 
of  the  earth,  and  so  far  as  concerns  the  motion  they  might  be  fastened  to- 
gether by  a  rigid  bar." — p.  277. 

In  this  argument  the  professor  does  not  indicate  that  the  present  motion 
of  the  moon  is  other  than  that  most  usually  indicated  in  the  books,  namely 
a  motion  of  the  moon  around  the  earth  in  a  closed  ellipse.    Nor  does  he  indi- 


36 

cate  when  the  present  mode  of  motion  of  the  moon  began,  nor  when  it  will 
end.  But  he  does  emphatically  say  that  when  the  moon  was  nearly  touching 
the  earth  the  two  went  round  each  other  like  a  dumb-bell  pivoted  in  the 
handle  and  that  in  the  end  they  will  go  round  in  the  same  way,  except  that 
the  handle  of  the  dumb-bell  will  be  very  much  longer. 

But  the  moon  does  not  move  about  the  earth  in  that  manner  )ww. 

Flammarion  described  the  present  mode  of  motion  of  the  moon  and 
claims  to  be  the  first  to  correctly  describe  that  motion. 

He  said: 

"A  rather  curious  fact  generally  forgotten  is  that  this  sinuous  curve  is 
so  elongated  that  it  scarcely  ditt'ers  from  that  which  the  earth  annually 
describes  round  the  sun;  and  instead  of  being  (as  it  is  always  drawn  in 
astronomical  treatises)  convex  to  the  sun,  at  the  epoch  of  every  new  moon, 
it  is  always  concave  to  the  sun!  I  have  represented  it  exactly  (Fig.  42)  on 
the  scale  of  1  millimetre  to  100,000  leagues.  In  this  figure  the  arc  of  the 
terestrial  orbit  is  drawn  with  an  opening  of  the  compass  of  37  centimetres 
for  37  millions." — 1  (In  a  note  he  says)  : 

"Tliis  true  form  of  the  lunar  orbit  was  drawn  for  the  first  time  in  1876  in 
the  first  edition  of  our  Terres  du  del." — Flammarion  Pop.  Ast.,  p.  108. 

Proctor  was  particularly  careful  to  illustrate  and  describe  the  path  of 
the  moon  about  the  earth  correctly.  He,  indeed,  classes  the  moon  as  a 
planet  which  travels  in  the  same  orbit  as  the  earth. — Old  and  New  Astron- 
omy, p.  492. 

Perhaps  he  was  so  careful  because  he  had  scolded  the  "paradoxists"  so 
vigorously  in  his  "Myths  and  Marvels  of  Astronomy,"  p.  274,  while  at  the 
same  time  admitting  that  the  fault  laj^  with  the  text  writers.  He  did  not 
effect  a  reform  in  that  respect.  Holden's  Astronomy,  published  in  1899, 
by  Henry  Holt,  pp.  216  and  217,  repeats  the  old  error  by  description  and 
illustration. 

But  the  books  do  not  give  the  figures  which  show  simply  the  real  path 
and  elements  of  the  moon's  motion.  As  that  is  the  foundation  upon  which 
I  wish  to  build  I  will  briefly  outline  the  figures. 

The  geocentric  longitude  and  radial  distances  of  the  moon  are  facts  of 
observation.  Let  us  assiune  that  the  earth  is  motionless  for  27  Va  days,  and 
that  the  moon  starts  a  "revolution"  of  the  earth  at  longitude  90°  while  in 
perigee  there.  Calculating  the  position  of  the  moon  for  each  two  days  Ave 
will  get  columns  1  to  9  of  Table  IV,  appendix.  By  plotting  the  figures 
of  cols.  5,  6  and  9  we  get  points  in  a  closed  ellipse. 

Now  let  us  give  the  earth  its  motion  and  assume  it  to  travel  in  a  straight 
line  towards  longitude  270'^,  and,  adding  that  motion  for  each  two  days  to 
the  moon's  ordinates,  which  lie  in  the  major  axis  of  the  ellipse,  we  get 
columns  10  and  11  of  the  same  tal)le.  Plotting  colunnis  5,  6  and  11  of  the 
table  we  get  the  actual  path  of  the  moon  about  the  earth,  namely  a  serpen- 


37 

tine  curve  formed  of  two  ares,  one  on  each  side  of  the  earth's  path,  the 
chord  of  the  first  arc  being  about  97  times  lono:er  than  its  middle  ordinate. 
This  path  of  the  moon  is  like  that  of  Fig.  5,  illustrating  a  theoretical  patli 
for  iMercury. 

The  real  path  of  the  moon  is  not  a  closed  ellipse,  yet  it  is  derived  from  the 
theory  of  a  closed  elliptical  orbit. 

But  Professor  Darwin's  description  of  the  original  motion  of  the  earth 
and  moon,  immediately  after  their  separation,  calls  for  an  epicycle  curve; 
that  is,  if  the  planets  move  forward  with  the  sun  as  if  fastened  ivith  a  bar, 
the  earth  not  rotating.  If  the  bar  were  removed  we  can  easily  conceive 
them  moving  as  they  do  now,  no  matter  at  what  distance  they  were  sep- 
arated. But  the  original  mode  of  motion  of  the  moon  and  the  present  mode 
constitute  a  problem  in  planetary  evolution  which  we  may  well  leave  with 
Professor  Darwin. 

Does  Mercury  "revolve"  around  the  sun  or  does  it  circulate  about  it  as 
the  moon  now  circulates  about  the  earth? 

Is  the  path  of  Mercury,  as  seen  from  the  stars,  a  closed  ellipse,  or  an 
epicycle  which  completely  encircles  the  sun,  or  an  epicycle  which  does  not 
encircle  the  sun,  or  is  it  an  epicycle  of  any  sort  ? 

The  mathematical  theory  of  the  motion  of  Mercury,  as  of  all  the  other 
planets,  deals  with  them  as  if  they  moved  around  a  stationary  body,  the  sun, 
in  a  closed  ellipse.  And  as  the  observations  of  the  motions  of  the  planet 
in  their  orbits  can  be  reconciled  with  these  mathematical  theories  we  must 
conclude  tJiat  the  sun  does  not  move  or  else  that  these  theories  of  closed 
elliptical  orbits  can  be  reconciled  with  the  sun's  motion  in  the  same  way  as 
we  did  the  motion  of  the  moon  in  a  serpentine  path  about  the  earth. 

The  constants  of  observation  as  to  the  heliocentric  longitude  and  radial 
distance  of  Mercury  from  the  sun  and  the  plane  of  its  motion  are  facts. 

So  long  as  the  sun  was  conceived  to  be  an  island  in  space  around  which 
the  planetary  ships  coasted  the  course  of  Mercury  was  settled  as  a  closed 
ellipse. 

Let  us  continue  that  assumption  during  one  "revolution"  of  Mercury 
and  let  us  start  Mercury  at  90°  heliocentric  longitude,  and  from  that  point 
tabulate  its  courses  for  every  five  days,  except  the  last  course,  and  we  will 
get  columns  1  to  9  of  Table  V  of  the  appendix.  Plotting  the  figures  in 
columns  6,  7  and  9  we  get  points  in  a  closed  ellipse. 

Now  let  us  assume  that  the  sun  moves  at  a  uniform  speed  in  the  direc- 
tion from  90°  to  270°.  By  adding  that  motion  to  the  ordinates  of  Mer- 
cury, which  lie  in  the  path  of  the  sun's  motion,  for  each  five  days,  we  can 
examine  the  different  orbits  or  paths  which  ]\Iercury  would  pursue  based 
upon  the  different  rates  of  speed  assigned  to  the  sun. 

If  we  begin  at  the  slowest  speed,  that  given  by  Sir  John  Herschel,  5 
miles  a  second,  we  will  get  columns  10  and  11  of  Table  V.     By  plotting 


38 

these  figures,  with  cols.  5  and  6,  yield  a  true  epicycle  which  encircles  the 
sun,  and  by  repeating  the  path  for  264  days  we  see  the  planet  making 
loops  about  the  sun  and  crossing  its  own  path  on  the  6th  course  when  making 
its  21st  course.     See  Figure  2. 

But  such  an  orbit  is  declared  to  be  impossible  by  one  astronomer. — Corn- 
stock  Text  Book  of  Astronomy,  59-60. 

If  we  take  the  next  highest  rate  of  speed  for  the  sun,  between  11.8  and 
18.5  miles  a  second — say  16  miles  as  a  mean — and  tabulate  that  speed  we 
get  columns  12  and  13  of  Table  V.  Plotting  these  figures,  namely  columns 
5,  6,  12  and  13  of  Table  V,  (see  Figure  3),  we  get  a  large  curve  for  the 
first  9  courses  on  the  west  side  of  the  sun's  path,  then  a  small  loop  for 
the  remainder  of  the  planet's  journey,  the  loop  beginning  when  the  planet 
crosses  the  line  of  the  sun's  path.  On  the  13th  course  you  will  notice  that 
the  planet  makes  on  the  13th  course  but  about  one-fourth  of  the  distance 
that  it  made  on  the  first  course.  This  loop  in  Mercury's  path — "to  port" 
— is  like  that  famous  loop  made  by  Admiral  Schley  in  the  "Brooklyn"  at 
the  sea  battle  of  Santiago,  about  which  there  was  so  much  controversy. 

But  about  this  loop  in  the  path  of  Mercury,  upon  a  supposed  speed  of 
the  sun  at  16  miles  a  second,  or  11.8  miles,  or  14.5  miles,  or  18.5  miles,  all 
of  which  have  been  assigned,  there  should  he  no  controversy.  If  the  sun 
proceeds  to  its  "apex"  at  any  such  rate  then  Mercury  makes  such  a  loop, 
larger  or  smaller,  as  the  sun's  speed  varies,  between  those  figures,  and  that 
real  loop  should  be  observable  when  the  earth  is  on  the  line  of  the  sun's 
way  or  near  the  line,  at  90°  or  270°  heliocentric  longitudes.  Such  occa- 
sions often  happen.  Mercury  is  then  at  its  greatest  elongation.  Apparent 
loops  in  Mercury's  path  are  observed  soon  after  Mercury  has  commenced 
this  real  loop  and  before  it  is  finished,  and  such  apparent  loops  are  very 
large  and  open,  more  so  than  that  of  any  planet  except  that  of  Venus. 
— Proctor's  Old  and  New  Astronomy,  p.  158. 

Proctor  says:  "In  the  case  of  INIercury,  it  is  the  large  inclination  of 
the  planet's  path  to  the  eliptic  which  causes  the  loop  to  undergo  remark- 
able changes  of  shape." 

So  that  no  difficulty  ought  to  exist  in  observing  a  real  loop  if  any  such 
was  made.  But  as  none  has  been  observed  it  must  be  assumed  that  none 
is  so  made  and  it  follows  that  the  sun  does  not  move  at  any  such  rate  of 
speed. 

Tabulating  the  speed  of  the  sun  at  33  miles  a  second,  we  get  columns 
14  and  15  of  Table  V.  (Remember  the  speed  assigned  to  the  sun  by 
Rancken  was  28  miles  a  second  and  by  ^Madler  30  miles  a  second.) 

Plotting  the  path  upon  this  new  speed,  see  Figure  4,  we  get  a  peculiar 
figure.  The  first  13  courses  give  a  large  curve  on  the  west  side  of  the 
sun  crossing  the  line  on  the  9th  course.  At  the  beginning  of  the  14th 
course  Mercury  spins  around,  on  its  heel  as  it  were,  and  takes  up  a  new 


I 


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TKwTAiv^rtji,  \'4vt  1. 


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39 

course,  almost  retrograde  to  the  13th  course,  and  from  that  point  starts  a 
new  curve  like  that  of  the  previous  courses.  At  this  speed  of  33  miles 
Mercury  ceases  to  form  a  loop  in  its  path.  It  is  not  conceivable,  however, 
that  the  planet  actually  performs  such  a  maneuver. 

Assuming  that  the  sun  moves  0,000,000  miles  a  day,  69.4  miles  a  second, 
we  get  columns  16  and  17  of  Table  V,  which  yield,  by  plotting,  see  Figure 
5,  a  path  about  the  sun  like  that  of  the  moon  about  the  earth,  except  that 
the  chords  of  the  arcs  are  not  nearly  so  long  compared  with  tlie  middla 
ordinate. 

The  closed  elliptical  orbit  of  Mercury,  when  combined  with  the  sun's 
motion  at  a  certain  speed,  gives  the  same  results  as  we  obtain  for  the  moon. 

Therefore  no  ditHculty  is  encountered  with  the  elliptical  mathematical 
theory  when  combined  with  the  proper — shall  we  say  "critical"? — speed 
of  the  sun.  IMoreover,  at  that  speed,  69.4  miles  per  second,  all  of  the 
planets  will  be  found  pursuing  the  same  sort  of  a  path  about  the  sun  when 
the  tabling  of  their  "orbits"  is  made  upon  the  same  basis. 

We  have  seen  that  some  claim  is  made  that  the  sun  moves  150  miles  a 
second,  which  is  over  twice  as  great  a  speed  as  is  necessary  to  make  the 
paths  of  the  planets  serpentine  curves. 

There  is  nothing  about  the  speed  of  69.4  miles  a  second  which  is  im- 
probable. 

That  speed  would  require  2689  years  to  cover  one  light  year's  distance. 

Nor  is  it  true  that  all  celestial  bodies  move  in  elliptical  orbits.  The 
sun  is  not  known  to  so  move.  Nor  are  many  of  the  stars,  some  of  which 
have  very  great  proper  motion,  with  immense  velocity. — Newcomh's  Stars, 
p.  158. 

Maxwell  Hall  and  others  have  endeavored  to  assign  an  elliptical  orbit 
and  position  of  central  sun  with  the  modest  period  of  20  million  years  for 
one  revolution.  The  sun's  path  in  that  orbit  would  be  a  straight  line — 
humanly  speaking. 

Having,  therefore,  precedent  in  the  motions  of  the  sun  and  moon,  we  can 
say  that  not  all  of  the  members  of  the  solar  system  move  in  a  closed  ellipse, 
or  epicycle,  and  that  there  is  ground  for  dispute  that  any  of  the  planets 
so  move. 

There  are  some  conclusions  to  be  drawn  from  this  method  of  examina- 
tion. The  most  important  is  that,  as  the  sun's  plane  of  motion  is  the  prin- 
cipal plane  of  the  solar  system,  and  such  plane  determines  the  planes  of  the 
planets'  movements,  then  there  are  certain  rates  of  speed  of  the  sun 
which  cannot  be  reconciled  with  the  known  movements  of  the  planets. 

The  speed  of  the  sun  also  determines  the  actual  speed  of  the  planets. 
For  instance,  the  earth  is  ordinarily  said  to  move  in  its  orbit  at  18.5  miles 
a  second.  But  that  is  based  upon  the  assumption  that  the  orbit  is  a 
closed  ellipse  around  an  anchored  sun.     When  Ave  add  the  motion  of  the  sun 


40 

we  increase  to  an  extent,  dependent  upon  the  rate  of  speed  of  the  sun,  the 
velocity  of  the  earth,  which  it  is  therefore  certain  very  much  exceeds  18.5 
miles  a  second. 

Upon  the  actual  speed  of  the  sun  and  its  planets  depends  the  estimates 
of  force  exerted  by  one  upon  the  other  during  their  separated  or  com- 
bined actions  as  discussed  in  chapter  one. 

I'^pon  the  actual  position  of  the  principal  plane  of  the  solar  system,  and 
the  speed  in  that  plane,  as  well  as  the  direction  therein  of  the  moving 
bodies,  depends  all  those  estimates  of  energy  exerted  by  the  sun  upon 
the  planets  and  by  the  planets  upon  the  sun. 


APPENDIX. 


TABLE    I. 


Position  of  planets  in  heliocentric  lon- 
gitude on  January  1st  of  each  year 

Direction   and    dis- 
tance   from    sun    to 
center  of  gravity  of 
system 

Sun's  position  relative  to  its 

apex  and  to  center  of 

gravity 

Year 
B.  C. 

Jup. 

Sat. 

Ura. 

Nep. 

Direction 

in  heliocer 

trie  long 

1-  Distance 
in  miles 

On  the 
course, 
miles 

Off  the 
course, 
miles 

917 

62^ 

38° 

58° 

59° 

55° 

925,000 

+760,000 

W  535,000 

738 

94° 

66° 

105° 

90° 

87° 

910,000 

+910,000 

W    45,000 

560 

97° 

81° 

148° 

119° 

100° 

885,000 

+870,000 

E  155,000 

380 

160° 

130° 

199° 

152° 

154° 

890,000 

+390,000 

E  800,000 

202 

196° 

172° 

289° 

210° 

166.5° 

855,000 

+205,000 

E  830,000 

83 

53° 

110° 

15° 

70° 

75° 

905,000 

+870,000 

W  230,000 

Year, 

A.  D. 

93 

116° 

149° 

67° 

103° 

119° 

870,000 

+760,000 

E  420,000 

272 

148° 

176° 

114° 

134° 

151° 

895,000 

+440,000 

E  780,000 

451 

181° 

202° 

160° 

165° 

183° 

910,000 

—  40,000 

E  910,000 

630 

213° 

229° 

206° 

195° 

213° 

920,000 

—  55,000 

E  770,000 

809 

246° 

256° 

254° 

225° 

247° 

920,000 

—840,000 

E  375,000 

948 

144° 

154° 

130° 

168° 

149° 

920,000 

+500,000 

E  790,000 

988 

279° 

283° 

301° 

256° 

280° 

930,000 

—915,000 

W  150,000 

1127 

177° 

180° 

176° 

199° 

181° 

930,000 

—  20,000 

E  930,000 

1167 

311° 

309° 

348° 

286° 

309° 

910,000 

—705,000 

W  575,000 

1306 

231° 

217° 

227° 

231° 

226.5° 

934,000 

—700,000 

E  625,000 

1486 

272° 

246° 

275° 

263° 

263.5° 

925,000 

—920,000 

E     95,000 

1665 

304° 

274° 

322° 

293° 

295.5° 

905,000 

—820,000 

W   40,000 

1804 

202° 

172° 

197° 

236° 

199° 

880,000 

—280,000 

E  835,000 

1844 

335° 

298° 

1° 

323° 

327.5° 

880.000 

-^65,000 

W  750,000 

41 


TABLE    II. 


Position  of  planets  in  heliocentric  lon- 
gitude on  January  1st  of  each  year 

Direction   and    dis- 
tance   from    sun    to 
center  of  gravity  of 
system 

Sun's  position 
apex  and 
gra 

relative  to  its 
to  center  of 
/ity 

Year 

Jup. 

Sat. 

Ura. 

Nep. 

Direction 
in  heliocen-  Distance 
trie  long.      in  miles 

On  the 
course, 
miles 

Off  the 
course, 
miles 

A.  D. 

1480 

90  = 

173° 

249° 

250° 

150° 

435,000 

1 

+280,000 

1 

E  330,000 

1481 

121° 

185° 

254° 

252° 

164° 

580,000 

+155,000 

E  550,000 

1482 

151° 

197° 

258° 

254° 

186° 

700,000 

—  30,000 

E  700,000 

1483 

181° 

209° 

262° 

257° 

206° 

805,000 

—350,000 

E  725,000 

1484 

212° 

222° 

267° 

259° 

226° 

890,000 

—635,000 

E  620,000 

1485 

242° 

234° 

271° 

261° 

245° 

925,000 

—840,000 

E  395,000 

1486 

272° 

246° 

275° 

263° 

263° 

925,000 

—920,000 

E     95,000 

1487 

303° 

258° 

280° 

265° 

283° 

880,000 

—860,000 

W  190,000 

1488 

333° 

270° 

284° 

268° 

302° 

810.000 

—690,000 

W  430,000 

1489 

3° 

283° 

288° 

270° 

320° 

700,000 

-^45,000 

W  540,000 

1490 

34° 

295° 

292° 

272° 

340° 

555,000 

—190,000 

W  520,000 

1491 

64° 

307° 

297° 

274° 

358° 

400,000 

—  15,000 

W  400,000 

1492 

94° 

319° 

301° 

276° 

19° 

225,000 

+  75,000 

W  210,000 

1493 

125° 

332° 

305° 

278° 

61° 

50,000 

+  45,000 

W    25,000 

1494 

155° 

344° 

310° 

281° 

224° 

120,000 

—  80,000 

E     85,000 

1495 

185° 

356° 

314° 

283° 

256° 

290,000 

—260,000 

E  120,000 

1496 

216° 

8° 

318° 

285° 

267° 

435,000 

—430,000 

E     30,000 

1497 

246° 

21° 

323° 

287° 

286° 

550,000 

—530,000 

W  145,000 

1498 

277° 

33° 

327° 

289° 

307° 

630,000 

—510,000 

W  375,000 

1499 

307° 

45° 

331° 

292° 

327° 

690,000 

—380,000 

W  575,000 

1500 

337° 

58° 

335° 

294° 

348.5° 

700,000 

—140,000 

W  690,000 

1501 

8° 

70° 

339° 

295° 

15.5° 

690,000 

+130,000 

W  680,000 

1502 

38° 

82° 

343° 

297° 

35.5° 

660,000 

+380,000 

W  535,000 

1503 

68° 

94° 

347° 

299° 

60° 

610,000 

+625,000 

W  300,000 

1504 

99° 

106° 

352° 

302° 

88.5° 

560,000 

+560,000 

W    15.000 

42 


Table  II  (Continued). 


Position  of  planets  in  heliocentric  lon- 
gitude on  January  1st  of  each  year 

Direction   and    dis- 
tance   from    sun    to 
center  of  gravity  of 
system 

Sun's  position  relative  to  its 

apex  and  to  center  of 

gravity 

Year 

Jup. 

Sat. 

Ura. 

Nep. 

Direction 
in  heliocen-  Distance 
trie  long.      in  mile;? 

On  the 
course, 
miles 

Off  the 
c<iurse, 
miles 

1505 

129^ 

118° 

356° 

304° 

119°       515,000  j 

+455,000 

E  250,000 

1506 

159° 

130° 

0° 

306° 

151.5°  490,000 

+235,000 

E  425,000 

1507 

190° 

143° 

5° 

308° 

184°       485,000 

—  35,000 

E  480,000 

1508 

220° 

155° 

9° 

310° 

214°       500,000 

—280,000 

E  410,000 

1509 

250° 

167° 

13° 

312° 

244°       520,000 

—465,000 

E  230,000 

1510 

281° 

179° 

18° 

314° 

271°       530.000 

—530,000 

W    10,000 

1511 

311° 

191° 

22° 

316° 

296.5°  520,000 

465,000 

W  230,000 

1512 

341° 

204° 

26° 

319° 

320°       505,000 

—320,000 

W  390,000 

1513 

12° 

216° 

30° 

321° 

345.5°  440,000 

—105,000 

W  425,000 

1514 

42° 

228° 

35° 

323° 

12.5°  355,000 

+  75,000 

W  345,000 

1515 

72° 

240° 

39° 

326° 

45°       270,000 

+190,000 

W  190,000 

1516 

103° 

253° 

43° 

328° 

90°       190,000 

+185,000 

0    00 

1517 

133° 

265° 

47° 

330° 

157°       175,000 

+  80,000 

E  165,000 

1518 

164° 

277° 

52° 

332° 

209°       270,000 

—125,000 

E  235,000 

1519 

194° 

290° 

56° 

334° 

241°       390,000 

—340,000 

E  180,000 

1520 

224° 

301° 

60° 

336° 

266°       525,000 

—520,000 

E     35,000 

1521 

255° 

314° 

65° 

339° 

295.5°  640,000 

—600,000 

W  215,000 

1522 

285° 

326° 

69° 

341° 

311.5°  745.000 

—560,000 

W  490,000 

1523 

315° 

338° 

73° 

343° 

331.5°  815,000 

—390,000 

W  710,000 

1524 

346° 

350° 

77° 

345° 

352.5°  865,000 

—115,000 

W  850,000 

1525 

16° 

3° 

82° 

347° 

12.5°  865,000 

+180,000 

W  845,000 

1526 

46° 

15° 

86° 

350° 

32°       845,000 

+450,000 

W  715,000 

1527 

77° 

27° 

90° 

352° 

53.5°  780,000 

+665,000 

W  465,000 

1528 

107° 

40° 

95° 

354° 

74°       695,000 

+625,000 

W  190,000 

1529 

137° 

52° 

99° 

356° 

95°       585,000 

+580,000 

E     60,000 

1530 

168° 

64° 

103° 

.358° 

119°       450,000 

+395,000 

E  215,000 

1531 

198° 

76° 

107° 

0° 

145°       315.000 

+  180,000 

E  255,000 

1532 

228° 

88° 

112° 

2° 

181°       185,000 

0  000 

E  190,000 

1533 

259° 

101° 

116° 

4° 

264°       135,000 

—130,000 

E     35,000 

1534 

289° 

113° 

120° 

7° 

320°       190,000 

—120,000 

W  150,000 

1535 

319° 

125° 

125° 

9° 

358°       300,000 

—  10,000 

W  300,000 

1536 

350° 

137° 

129° 

11° 

26°       400,000 

+  170,000 

W  355,000 

1537 

20° 

149° 

133° 

13° 

51.5°  480,000 

+370,000 

W  300,000 

1538 

51° 

162° 

137° 

15° 

76.5°  535,000 

+520,000 

W  130,000 

1539 

81° 

174° 

142° 

17° 

100.5°  585,000 

+570,000 

E  105,000 

1540 

111° 

186° 

146° 

20° 

124.5°  610,000 

+500,000 

E  345,000 

1541 

142° 

198° 

150° 

22° 

150°       620.000 

+310,000 

E  540,000 

43 


Table 

II  (Continutd). 

Position  of  planets  in 
gitude  on  January  Is 

lieliocentric  lon- 
5t  of  eacli  year 

Direction   and    dis- 
tance   from   sun    to 
center  of  gravity  of 
system 

Sun's  position  relative  to  its 

apex  and  to  center  of 

gravity 

Year 

J  up. 

Sat. 

Ura. 

Nep. 

Direction 
in  heliocen-  Distance 
trie  long.      in  miles 

On  the 
course, 
miles 

Off  the 
course, 
miles 

1542 

172° 

211° 

155° 

24° 

178°       615,000 

4-  20,000 

E  615,000 

1543 

202° 

223° 

159° 

26° 

202°       615,000 

—240,000 

E  565,000 

1544 

233° 

235° 

163° 

28° 

231.5°  610,000 

—480,000 

E  375,000 

1545 

263° 

247° 

167° 

31° 

261°       610,000 

—600,000 

E  110,000 

1546 

293° 

259° 

172° 

33° 

285.5°  605,000 

—585,000 

W  160,000 

1547 

324° 

272° 

176° 

35° 

313.5°  605,000 

—440,000 

W  420,000 

1548 

354° 

284° 

180° 

37° 

338.5°  595,000 

—215,000 

W  550,000 

1549 

24° 

296° 

185° 

39° 

4°       560,000 

+  35,000 

W  560,000 

1550 

55° 

308° 

189° 

41° 

30°       515,000 

+225,000 

W  440,000 

1551 

85° 

321° 

193° 

44° 

56°       460,000 

+380,000 

W  260,000 

1552 

115° 

333° 

197° 

46° 

83°       380,000 

+375,000 

W    50,000 

1553 

146° 

345° 

202° 

48° 

114°       290,000 

+265,000 

E  120,000 

1554 

176° 

357° 

206° 

50° 

154°       215,000 

+  95,000 

E  190,000 

1555 

206° 

9° 

210° 

53° 

214°       175,000 

—  95,000 

E  140,000 

1556 

237° 

22° 

215° 

55° 

270°       220,000 

—220,000 

0    000 

1557 

267° 

34° 

219° 

57° 

310°       345,000 

—270,000 

W  215,000 

1558 

298° 

46° 

223° 

59° 

337.5°  435,000 

—165,000 

W  400,000 

1559 

328° 

58° 

227° 

61° 

3.5°  540,000 

+  30,000 

W  550,000 

1560 

358° 

70° 

232° 

63° 

26°       625,000 

+275,000 

W  560,000 

1561 

29° 

83° 

236° 

66° 

50°       690,000 

+530,000 

W  440,000 

1562 

59° 

95° 

240° 

68° 

72°       740,000 

+640,000 

W  230,000 

1563 

89° 

107° 

245° 

70° 

94°       765.000 

+765,000 

E     50,000 

1564 

120° 

119° 

249° 

72° 

116.5°  760,000 

+680,000 

E  340,000 

1565 

150° 

131° 

253° 

74° 

139°       730,000 

+480,000 

E  550,000 

1566 

180° 

144° 

257° 

77° 

163°       685,000 

+205,000 

E  655,000 

1567 

211° 

156° 

262° 

79° 

187°       620,000 

—  75,000 

E  610,000 

1568 

241° 

168° 

266° 

81° 

213.5°  540,000 

—290,000 

E  450,000 

1569 

271° 

180° 

270° 

83° 

241°       460,000 

■ 

—405,000 

E  220,000 

1570 

302° 

192° 

275° 

85° 

271°       390,000 

—390,000 

W    10,000 

1571 

332° 

205° 

279° 

87° 

307.5°  330,000 

—220,000 

W  200,000 

1572 

2° 

217° 

283° 

90° 

345°       290,000 

—  75,000 

W  275,000 

1573 

33° 

229° 

287° 

92° 

20°       290,000 

+  95,000 

W  270.000 

1574 

63° 

241° 

292° 

94° 

43°       165,000 

+110,000 

W  120,000 

1575 

93° 

254° 

296° 

96° 

104°       295,000 

+285,000 

E     70,000 

1576 

124° 

266° 

300° 

98° 

143°       325,000 

+190,000 

E  265,000 

1577 

154° 

278° 

305° 

101° 

177°       370,000 

+  20,000 

E  370,000 

1578 

184° 

291° 

309° 

103° 

208.5°  400,000 

—  30,000 

E  355,000 

44 


Table 

II  (Con 

tinned). 

Position  of  planets  in 
gitude  on  January  Is 

bieliocentric  lon- 
t  of  each  year 

Direction   and    dis- 
tance   from    sun    to 
center  of  gravity  of 
system 

Sun's  position  relative  to  its 

apex  and  to  center  of 

gravity 

Year 

Jup. 

Sat. 

Ura. 

Nep. 

Direction 
in  heliocen-  Distance 
trie  long.      in  miles 

On  the 
course, 
miles 

Off  the 

course, 

miles 

1579 

215° 

302° 

313° 

105° 

241° 

420,000 

—370,000 

E  200,000 

1580 

245° 

315° 

317° 

107° 

270° 

520,000 

—520,000 

0    000 

1581 

275° 

327° 

322° 

109° 

297° 

570,000 

—515,000 

W  260,000 

1582 

306° 

339° 

326° 

111° 

323° 

645.000 

—390.000 

W  510,000 

1583 

336° 

351° 

330° 

114° 

347.5° 

690,000 

—150,000 

W  675,000 

1584 

6° 

4° 

335° 

116° 

12.5° 

735,000 

+160,000 

W  715,000 

1585 

37° 

16° 

339° 

118° 

36° 

750,000 

+435,000 

W  610,000 

1586 

67° 

28° 

343° 

120° 

57° 

755,000 

+630,000 

W  410,000 

1587 

97° 

41° 

347° 

122° 

81° 

720,000 

+710,000 

W  115,000 

1588 

128° 

53° 

352° 

125° 

101° 

680,000 

+670,000 

E  130.000 

1589 

158° 

65° 

356° 

127° 

122.5° 

605,000 

+505.000 

E  330,000 

1590 

188° 

77° 

0° 

129° 

144° 

500,000 

+290,000 

E  410,000 

1591 

219° 

89° 

5° 

131° 

167.5° 

375,000 

+  80,000 

E  370,000 

1592 

249° 

102° 

9° 

133° 

197° 

250,000 

—  70,000 

E  235,000 

1593 

279° 

114° 

13° 

136° 

239.5° 

120,000 

—105,000 

E     55,000 

1594 

310° 

126° 

18° 

138° 

342° 

120,000 

—  40,000 

W  115,000 

1595 

340° 

138° 

22° 

140° 

31° 

245,000 

+125,000 

W  210,000 

1596 

11° 

150° 

26° 

142° 

60° 

390,000 

+325,000 

W  195,000 

1597 

41° 

163° 

30° 

144° 

82° 

495,000 

+490,000 

W    70,000 

1598 

72° 

175° 

35° 

146° 

105° 

610,000 

+585,000 

E  160,000 

1599 

102° 

187° 

39° 

149° 

127° 

675.000 

+640,000 

E  400,000 

1600 

132° 

200° 

43° 

151° 

150° 

720,000 

+370,000 

E  620,000 

1601 

163° 

212° 

47° 

153° 

170° 

740,000 

+125,000 

E  730,000 

1602 

193° 

224° 

52° 

155° 

193° 

745,000 

—170,000 

E  725,000 

1603 

223° 

236° 

56° 

157° 

215° 

695,000 

400,000 

E  565,000 

1604 

254° 

248° 

60° 

160° 

239° 

620,000 

—535,000 

E  315,000 

1605 

284° 

260° 

65° 

162° 

266° 

565,000 

—565,000 

E     45,000 

1606 

314° 

273° 

69° 

164° 

294° 

500,000 

455.000 

W  200,000 

1607 

345° 

285° 

73° 

166° 

327.5° 

465,000 

—250,000 

W  395,000 

1608 

15° 

297° 

77° 

168° 

360° 

445,000 

0  000.000 

W  445.000 

1609 

45° 

309° 

82° 

171° 

33.5° 

425,000 

+235,000 

W  350,000 

1610 

76° 

322° 

86° 

173° 

65° 

430,000 

+390,000 

W  180,000 

1611 

106° 

334° 

90° 

175° 

96° 

425,000 

+420,000 

E     45,000 

1612 

136° 

346° 

95° 

177° 

124° 

420,000 

+350,000 

E  235,000 

1613 

167° 

358° 

99° 

179° 

153° 

395,000 

+175,000 

E  350,000 

1614 

197° 

10° 

103° 

181° 

182° 

355,000 

—  10,000 

E  350.000 

1615 

227° 

23° 

107° 

184° 

214° 

305,000 

—170.000 

E  250.000 

45 


Table  II  (Continued). 


Position  of  planets  in 

heliocentric  lon- 

Direction   and    dis- 
tance   from   sun    to 

Sun's  position 

relative  to  its 

gitude  on  January  1st  of  eacli  year 

center  of  gravity  of 
system 

apex  and  to  center  of 
gravity 

Direction 

On  the 

Off  the 

Year 

Jup. 

Sat. 

Ura. 

Nep. 

in  iieliocen-  Distance 
trie  long.      in  miles 

course, 
miles 

course, 
miles 

1616 

258° 

35° 

112° 

186° 

257°       230,000 

—225,000 

E     50,000 

1617 

288° 

47° 

116° 

188° 

287°       245,000 

—200,000 

W  140,000 

1618 

318° 

59° 

120° 

190° 

351°       395,000 

—  45,000 

W  290,000 

1619 

349° 

72° 

125° 

192° 

29.5°  380,000 

4-185,000 

W  340,000 

1620 

19° 

84° 

129° 

195° 

57°       505,000 

+425,000 

W  270,000 

1621 

49° 

96° 

133° 

197° 

82.5°  625,000 

+620,000 

W    80,000 

1622 

80° 

108° 

137° 

199° 

104.5°  690,000 

+670,000 

E  170,000 

1623 

110° 

120° 

142° 

201° 

127°       815,000 

+650,000 

E  485,000 

1624 

140° 

133° 

146° 

203° 

147.5°  870,000 

+470,000 

E  730,000 

1625 

171° 

145° 

150° 

205° 

167.5°  890,000 

+195,000 

E  865,000 

1626 

201° 

157° 

155° 

208° 

186.5°  870,000 

—100,000 

E  855,000 

1627 

231° 

169° 

159° 

210° 

205°       825,000 

—350,000 

E  740,000 

1628 

262° 

181° 

163° 

212° 

224.5°  730,000 

—505,000 

E  520,000 

1629 

292° 

194° 

167° 

214° 

243.5°  620,000 

—550,000 

E  280,000 

1630 

322° 

206° 

172° 

216° 

262°       480,000 

—475,000 

E     30,000 

1631 

353° 

218° 

176° 

219° 

282°       305,000 

—300,000 

W    60,000 

1632 

23° 

230° 

180° 

221° 

303°       130,000 

—110,000 

W    70,000 

1633 

53° 

243° 

185° 

223° 

124.5°     45,000 

+  35,000 

E     25,000 

1634 

84° 

255° 

189° 

225° 

254°       230,000 

+100,000 

E  200,000 

1635 

114° 

267° 

193° 

227° 

174°       275,000 

+  40,000 

E  380,000 

1636 

144° 

279° 

197° 

229° 

193°       515,000 

—115,000 

E  500,000 

1637 

175° 

291° 

202° 

232° 

213°       635,000 

—345,000 

E  530,000 

1638 

205° 

304° 

206° 

234° 

232°       710,000 

—560,000 

E  435,000 

1639 

235° 

315° 

210° 

236° 

252°       750,000 

—710,000 

E  240,000 

1640 

266° 

328° 

215° 

238° 

277°       760,000 

—760,000 

W    30,000 

1641 

296° 

340° 

219° 

240° 

293°       740,000 

—680,000 

W  295,000 

1642 

326° 

353° 

223° 

243° 

316.5°  695,000 

—480,000 

W  500,000 

1643 

357° 

5° 

227° 

245° 

342°       625,000 

—190,000 

W  590,000 

1644 

27° 

17° 

232° 

247° 

8.5°  550,000 

+  80,000 

W  545,000 

1645 

57° 

29° 

236° 

249° 

38.5°  485,000 

+300,000 

W  375,000 

1646 

88° 

42° 

240° 

251° 

74°       430,000 

+415,000 

W  110,000 

1647 

118° 

54° 

245° 

253° 

110°       425,000 

+395,000 

E  145,000 

1648 

148° 

66° 

249° 

256° 

144°       435,000 

+250,000 

E  355,000 

1649 

179° 

78° 

253° 

258° 

176°       460,000 

+  25,000 

E  465,000 

1650 

209° 

90° 

257° 

260° 

204°       485,000 

—195,000 

E  445,000 

1651 

239° 

103° 

262° 

262° 

230°       500,000 

—375,000 

E  325,000 

1652 

270° 

115° 

266° 

264° 

255°       480,000 

—460,000 

E  130,000 

46 


Table 

II  (Continued). 

Position  of  planets  in 
gitude  on  January  Is 

leliocentric  lon- 
t  of  each  year 

Direction   and    dis- 
tance   from    sun    to 
center  of  gravity  of 
system 

Sun's  position 

apex  and   t 

gra\ 

relative  to  its 
o  center  of 
•ity 

Direction 

On  the 

Off  the 

Year 

J  up. 

Sat. 

Ura. 

Nep. 

in  heliocen-  Distance 
trie  long.      in  miles 

course, 
miles 

course, 
miles 

1G53 

300° 

127° 

270° 

267° 

280°       435,000 

—430,000 

W    70,000 

1654 

330° 

139° 

275° 

269° 

304°       365,000 

—300,000 

W  210,000 

1655 

1° 

151° 

279° 

271° 

340°       275,000 

—100,000 

W  250,000 

1656 

sr 

164° 

283° 

273° 

24.5°  195,000 

+  80,000 

W  180,000 

1657 

61° 

176° 

287° 

275° 

86°       195,000 

+200,000 

W    10,000 

1658 

92° 

188° 

292° 

277° 

137.5°  305,000 

+205,000 

E  220,000 

1659 

122° 

200° 

296° 

280° 

168°       440,000 

+  90,000 

E  425,000 

1660 

152° 

213° 

300° 

282° 

193°       570,000 

—130,000 

E  550,000 

1661 

183° 

225° 

305° 

284° 

216.5°  695,000 

415,000 

E  550,000 

1662 

213° 

237° 

309° 

286° 

237°       795,000 

—665,000 

E  430,000 

1663 

343° 

249° 

313° 

288° 

257°       865,000 

—840,000 

E  200,000 

1664 

274° 

261° 

317° 

291° 

276.5°  900,000 

—900,000 

W  100,000 

1665 

304° 

274° 

322° 

293° 

295.5°  905,000 

—820,000 

W  400,000 

1666 

334° 

286° 

326° 

295° 

313.5°  865,000 

—625,000 

W  610,000 

1667 

5° 

298° 

330° 

297° 

334°       795,000 

—390,000 

W  715,000 

1668 

35° 

310° 

335° 

299° 

352°       685,000 

—  95,000 

W  680,000 

1669 

66° 

323° 

339° 

302° 

12°       555,000 

+115,000 

W  540,000 

1670 

96° 

335° 

343° 

304° 

31.5°  400,000 

+210,000 

W  335,000 

1671 

126° 

347° 

347° 

306° 

53°       225,000 

+175,000 

W  135,000 

1672 

157° 

359° 

352° 

308° 

96°         50,000 

+  50,000 

E       5,000 

1673 

187° 

11° 

356° 

310° 

253°       135,000 

—130,000 

E     40,000 

1674 

218° 

24° 

0° 

312° 

287.5°  280,000 

—275,000 

W    35,000 

1675 

248° 

36° 

5° 

314° 

300°       430,000 

—375,000 

W  210,000 

1676 

279° 

48° 

9° 

316° 

319.5°  550,000 

—355,000 

W  420,000 

1677 

309° 

60° 

13° 

319° 

341°       620,000 

—215,000 

W  600,000 

1678 

339° 

73° 

18° 

321° 

1°       690,000 

+  15,000 

W  690,000 

1679 

10° 

85° 

22° 

323° 

12°       725,000 

+270,000 

W  670,000 

1680 

40° 

97° 

26° 

326° 

44°       710,000 

+475,000 

W  490,000 

1681 

70° 

109° 

30° 

328° 

67°       695,000 

+640,000 

W  275,000 

1682 

101° 

121° 

35° 

330° 

92.5°  640,000 

+640,000 

E     30.000 

1683 

131° 

134° 

39° 

332° 

117°       580,000 

+515,000 

E  275,000 

1684 

161° 

146° 

43° 

334° 

148°       530,000 

+280,000 

E  450,000 

1685 

192° 

158° 

47° 

336° 

181°       500,000 

—     5,000 

E  495,000 

1686 

222° 

170° 

52° 

339° 

212°       480,000 

—250,000 

E  410,000 

1687 

252° 

182° 

56° 

341° 

243°       475,000 

425,000 

E  215,000 

1688 

283° 

195° 

60° 

343° 

275°       480,000 

—490,000 

W    30,000 

1689 

313^^ 

207° 

65° 

345° 

302°       480.000 

—410,000 

W  250,000 

47 


Table 

II  (Contmued). 

Direction   and    dis- 

Position of  planets  in 

heliocentric  lon- 

tance    from   sun    to 

Sun's  position 

relative  to  its 

gitude  on  January  1st  of  each  year 

center  of  gravity  of 
system 

apex  and  to  center  of 
gravity 

Direction 

On  the 

Off  the 

Year 

Jup. 

Sat. 

Ura. 

Nep. 

in  heliocen-  Distance 
trie  long.      in  miles 

course, 
miles 

course, 
miles 

1690 

343° 

219° 

69° 

347° 

329°       490,000 

—250,000 

W  420,000 

1691 

14° 

231° 

73° 

350° 

356.5°  460,000 

—  30,000 

W  450,000 

1692 

44° 

244° 

77° 

352° 

23°       415,000 

+155,000 

W  385,000 

1693 

74° 

256° 

82° 

354° 

51°       340,000 

+265,000 

W  210,000 

1694 

105° 

268° 

86° 

356° 

85°       265,000 

+260,000 

W    20,000 

1695 

135° 

280° 

90° 

358° 

130°       210,000 

+160,000 

E  135,000 

1696 

165° 

292° 

95° 

0° 

188°       215,000 

—  30,000 

E  215,000 

1697 

196° 

305° 

'99° 

2° 

237°       300,000 

—255,000 

E  165,000 

1698 

226° 

316° 

103° 

4° 

268°       415,000 

-—110,000 

E     10,000 

1699 

256° 

329° 

107° 

7° 

294°       425,000 

—485,000 

W  210,000 

1700 

287° 

341° 

112° 

9° 

319°       645,000 

—425,000 

W  485,000 

1701 

317° 

354° 

116° 

11° 

341°       730,000 

—240,000 

W  690,000 

1702 

347° 

6° 

120° 

13° 

1.5°  795,000 

+  25,000 

W  790,000 

1703 

18° 

18° 

125° 

15° 

23°       830,000 

+315,000 

W  765,000 

1704 

48° 

30° 

129° 

17° 

42.5°  835,000 

+565,000 

W  615,000 

1705 

78° 

43° 

133° 

20° 

65°       830,000 

+750,000 

W  350,000 

1706 

109° 

55° 

137° 

22° 

85°       750,000 

+745,000 

W    70,000 

1707 

139° 

67° 

142° 

24° 

106°       660,000 

+635,000 

E  180,000 

1708 

169° 

79° 

146° 

26° 

126.5°  565,000 

+445,000 

E  340,000 

1709 

200° 

91° 

150° 

28° 

151.5°  435,000 

+205,000 

E  380,000 

1710 

230° 

104° 

155° 

31° 

180°       310,000 

0  000,000 

E  310,000 

1711 

260° 

116° 

159° 

33° 

219°       195,000 

—120,000 

E  145,000 

1712 

291° 

128° 

163° 

35° 

288°       135,000 

—130,000 

W    45,000 

1713 

321° 

140° 

167° 

37° 

352°       200,000 

—  25,000 

W  195,000 

1714 

351° 

152° 

172° 

39° 

30°       305,000 

+  150,000 

W  260,000 

1715 

22° 

165° 

176° 

41° 

55°       355,000 

+290,000 

W  210,000 

1716 

52° 

177° 

180° 

44° 

84°       480,000 

+470,000 

W    45,000 

1717 

82° 

189° 

185° 

46° 

107°       535,000 

+510,000 

E  195,000 

1718 

113° 

201° 

189° 

48° 

133°       580,000 

+420,000 

E  400,000 

1719 

143° 

214° 

193° 

50° 

158.5°  610,000 

+220,000 

E  565,000 

1720 

174° 

226° 

197° 

53° 

184°       630,000 

—  50,000 

E  625,000 

1721 

204° 

238° 

202° 

55° 

210°       630,000 

—310,000 

E  550,000 

1722 

234° 

250° 

206° 

57° 

235°       635,000 

—525,000 

E  360,000 

1723 

265° 

262° 

210° 

59° 

263°       630,000 

—625,000 

E     80,000 

1724 

295° 

275° 

215° 

61° 

290°       630,000 

—595,000 

W  205,000 

1725 

325° 

287° 

219° 

63° 

315°       625,000 

—440,000 

W  440,000 

1726 

356° 

299° 

223° 

66° 

335°       620,000 

—260,000 

W  565,000 

48 


Table  II  (Continued). 

Position  of  planets  in  heliocentric  lon- 
gitude on  January  1st  of  each  year 

Direction  and  dis- 
tance from  sun  to 
center  of  gravity  of 
system 

Sun's  position  relative  to  its 

apex  and  to  center  of 

gravity 

Year 

Jup. 

Sat. 

Ura. 

Nep. 

Direction 
in  heliocen-  Distance 
trie  long.   in  miles 

On  the 
course, 
miles 

Off  the 

course, 

miles 

1727 

26^ 

311° 

227° 

6S° 

8° 

575,000 

+  80,000 

W  570.000 

1728 

56° 

324° 

232° 

70° 

33° 

555,000 

+300,000 

W  465,000 

1729 

86" 

336° 

236° 

72° 

58° 

500,000 

+425,000 

W  265,000 

1730 

117° 

348° 

240° 

74° 

86° 

430,000 

+430,000 

W  30,000 

1731 

147° 

0° 

245° 

77° 

113° 

345,000 

+310,000 

E  135,000 

1732 

177° 

12° 

249° 

79° 

148° 

255,000 

+  135,000 

E  215.000 

1733 

208° 

25° 

253° 

81° 

195° 

185,000 

—  50,000 

E  180,000 

1734 

238° 

37° 

257° 

83° 

262° 

185,000 

—185,000 

E  25,000 

1735 

268° 

49° 

262° 

85° 

304° 

260,000 

—210,000 

W  150,000 

1736 

299° 

61° 

266° 

87° 

340° 

365,000 

—130,000 

W  345,000 

1737 

329° 

74° 

270° 

90° 

8° 

465,000 

+  60,000 

W  460,000 

1738 

0° 

86° 

275° 

92° 

33° 

570,000 

+215,000 

W  470.000 

1739 

30° 

98° 

279° 

94° 

56° 

640,000 

+540,000 

W  360,000 

1740 

60° 

110° 

283° 

96° 

79° 

715,000 

+700,000 

W  145,000 

1741 

91° 

122° 

287° 

98° 

101° 

725,000 

+710,000 

E  140.000 

1742 

122° 

135° 

292° 

101° 

123.5° 

760,000 

+630,000 

E  430,000 

1743 

152° 

147° 

296° 

103° 

145° 

730,000 

+420,000 

E  615,000 

1744 

182° 

159° 

300° 

105° 

168° 

705,000 

+140,000 

E  690,000 

1745 

213° 

171° 

305° 

107° 

192° 

650,000 

—140,000 

E  630,000 

1746 

243° 

183° 

309° 

109° 

218° 

575,000 

—350,000 

E  450,000 

1747 

273° 

196° 

313° 

111° 

245° 

500,000 

—455,000 

E  220,000 

1748 

304° 

208° 

317° 

114° 

278° 

420,000 

—420,000 

W  55,000 

1749 

334° 

220° 

322° 

116° 

308° 

365,000 

—285,000 

W  220,000 

1750 

4° 

232° 

326° 

118° 

345° 

315,000 

—  85,000 

W  305,000 

1751 

35° 

245° 

330° 

120° 

25° 

295,000 

+120,000 

W  265,000 

1752 

65° 

257° 

335° 

122° 

65° 

290,000 

+255,000 

W  125,000 

1753 

95° 

269° 

339° 

125° 

109° 

295,000 

+290,000 

E  35,000 

1754 

126° 

281° 

343° 

127° 

138° 

320,000 

+210,000 

E  235,000 

1755 

156° 

293° 

347° 

129° 

170° 

340,000 

+  50,000 

E  335,000 

1756 

186° 

306° 

352° 

131° 

205° 

360,000 

—155,000 

E  325,000 

1757 

217° 

317° 

356° 

133° 

240° 

405,000 

—350,000 

E  205.000 

1758 

247° 

330° 

0° 

136° 

272° 

445,000 

—445,000 

W  15.000 

1759 

277° 

342° 

5° 

138° 

301° 

510,000 

--435,000 

W  260,000 

1760 

308° 

355° 

9° 

140° 

330° 

570,000 

—280,000 

W  500,000 

1761 

338° 

7° 

13° 

142° 

356° 

645,000 

—  35,000 

W  640,000 

1762 

9° 

19° 

17° 

144° 

22° 

705,000 

+260,000 

W  655,000 

1763 

39° 

31° 

22° 

146° 

45° 

750,000 

+525,000 

W  535,000 

49 


Table  II  (Continutd). 


Position  of  planets  in  heliocentric  lon- 
gitude on  January  1st  of  each  year 


Year        Jup. 


Sat.        Ura. 


Nep. 


Direction   and    dis- 
tance   from   sun    to 
center  of  gravity  of 
system 


Direction 
in  iieliocen-  Distance 
trie  long.      in  miles 


Sun's  position  relative  to  its 

apex  and  to  center  of 

gravity 


On  the 
course, 

miles 


Off  the 

course, 

miles 


1764 

69  = 

44° 

26° 

149° 

67° 

770,000 

+715,000 

W  300,000 

1765 

100° 

56° 

30° 

151° 

89° 

765,000 

+765,000 

W  15,000 

1766 

130° 

68° 

35° 

153° 

112° 

725,000 

+675,000 

E  270,000 

1767 

160° 

80° 

39° 

155° 

131° 

660,000 

+505,000 

E  430,000 

1768 

191° 

92° 

43° 

157° 

152° 

600,000 

+280,000 

E  535,000 

1769 

221° 

105° 

47° 

160° 

173° 

500,000 

+  55,000 

E  490,000 

1770 

251° 

117° 

52° 

162° 

197° 

365,000 

—105,000 

E  350,000 

1771 

282° 

129° 

56° 

164° 

223° 

220,000 

—150,000 

160,000 

1772 

312° 

141° 

60° 

166° 

280° 

85,000 

—  80,000 

W  15,000 

1773 

342° 

154° 

65° 

168° 

33° 

135,000 

+  70,000 

W  95,000 

1774 

13° 

166° 

69° 

171° 

71° 

290,000 

+270,000 

W  110,000 

1775 

43° 

178° 

73° 

173° 

94° 

430,000 

+430,000 

E  30,000 

1776 

73° 

190° 

77° 

175° 

114° 

560,000 

+510,000 

E  235.000 

1777 

104° 

202° 

82° 

177° 

136° 

645,000 

+445,000 

E  465,000 

1778 

134° 

215° 

86° 

179° 

159° 

710,000 

+260,000 

E  665,000 

1779 

164° 

227° 

90° 

181° 

178° 

755,000 

+  20,000 

E  755,000 

1780 

195° 

239° 

95° 

184° 

199° 

770,000 

—250,000 

E  725,000 

1781 

225° 

251° 

99° 

186° 

222° 

745,000 

--190,000 

E  560,000 

1782 

255° 

263° 

103° 

188° 

244° 

710,000 

—640,000 

E  310,000 

1783 

286° 

276° 

107° 

190° 

268° 

645,000 

—645,000 

E  20,000 

1784 

316° 

288° 

112° 

192° 

295° 

570,000 

—520,000 

W  240,000 

1785 

346° 

300° 

116° 

195° 

324° 

495,000 

—300,000 

W  400,000 

1786 

17° 

312° 

120° 

197° 

357° 

435,000 

—  20,000 

W  435,000 

1787 

48° 

325° 

124° 

199° 

34° 

400,000 

+220,000 

W  330,000 

1788 

78° 

337° 

129° 

201° 

79° 

390,000 

+365,000 

W  140,000 

1789 

108° 

349° 

133° 

203° 

112° 

400,000 

+390,000 

E  85,000 

1790 

139° 

1° 

137° 

205° 

144° 

410,000 

+300,000 

E  280,000 

1791 

169° 

13° 

142° 

208° 

162° 

425,000 

+  130,000 

E  400,000 

1792 

199° 

25° 

146° 

210° 

179" 

420,000 

+  10,000 

E  420,000 

1793 

230° 

38° 

150° 

212° 

219° 

370,000 

—235,000 

E  290,000 

1794 

260° 

50° 

155° 

214° 

248° 

330.000 

—310,000 

E  120,000 

1795 

290° 

62° 

159° 

216° 

284° 

280,000 

—270,000 

W  65,000 

1796 

321° 

73° 

163° 

219° 

334° 

270,000 

—120,000 

W  245,000 

1797 

351° 

86° 

167° 

221° 

18° 

300,000 

+  90,000 

W  290.000 

1798 

21° 

99° 

172° 

223° 

58° 

385,000 

+325,000 

W  200,000 

1799 

51° 

111° 

176° 

225° 

88° 

500,000 

+500,000 

W  15,000 

1800 

81° 

123° 

180° 

227° 

113° 

615,000 

+560,000 

E  245,000 

50 


Table 

II  (Con 

tinucd). 

Position  of  planets  in  heliocentric  lon- 
gitude on  January  1st  of  each  year 

Direction  and  dis- 
tance from  sun  to 
center  of  gravit\-  of 
system 

Sun's  position  relative  to  its 

apex  and  to  center  of 

gravity 

Year 

Jup. 

Sat. 

Ura. 

Nep. 

Direction 
in  lieliocen-  Distance 
trie  long,   in  miles 

On  the 
course, 
miles 

Off  the 
course, 
miles 

1801 

111^ 

135° 

185° 

229° 

136° 

710,000 

-f490,000 

E  515,000 

1802 

142° 

147° 

189° 

232° 

158° 

795,000 

+300,000 

E  735,000 

1803 

172° 

160° 

193° 

234° 

179° 

850,000 

+  20,000 

E  850,000 

1804 

202° 

172° 

197° 

236° 

199° 

880,000 

—280,000 

E  835,000 

1805 

234° 

184° 

202° 

238° 

218° 

865,000 

—540,000 

E  680,000 

1806 

264° 

196° 

206° 

240° 

237° 

820,000 

—690,000 

E  445,000 

1807 

294° 

209° 

210° 

243° 

257° 

725,000 

—705,000 

E  180,000 

1808 

325° 

221° 

215° 

245° 

276° 

605,000 

—600,000 

W  55,000 

1809 

355° 

233° 

219° 

247° 

293.5° 

480,000 

—440,000 

W  195,000 

1810 

25° 

245° 

223° 

249° 

311° 

310,000 

—230,000 

W  205,000 

1811 

56° 

257° 

227° 

251° 

329° 

115,000 

—  60,000 

W  105,000 

1812 

86° 

270° 

232° 

253° 

171° 

60,000 

+  10,000 

E  60,000 

1813 

116° 

282° 

236° 

256° 

190° 

230,000 

—  40,000 

E  225,000 

1814 

147° 

294° 

240° 

258° 

209° 

395,000 

—190,000 

E  345,000 

1815 

177° 

306° 

245° 

260° 

228° 

550,000 

^00,000 

E  375,000 

1816 

207° 

319° 

249° 

262° 

245° 

650,000 

—585,000 

E  275,000 

1817 

238° 

331° 

253° 

264° 

265° 

740,000 

—740,000 

E  60,000 

1818 

268° 

343° 

257° 

267° 

285° 

780,000 

—760,000 

W  205,000 

1819 

298° 

355° 

262° 

269° 

305° 

800,000 

—660,000 

W  455,000 

1820 

329° 

7° 

266° 

271° 

326° 

770,000 

—435,000 

W  640,000 

1821 

359° 

20° 

270° 

273° 

348° 

730,000 

—145,000 

W  715,000 

1822 

30° 

32° 

274° 

275° 

12° 

650,000 

+135,000 

W,635,000 

1823 

60° 

44° 

279° 

277° 

38° 

570,000 

+355,000 

W  440,000 

1824 

90° 

56° 

283° 

280° 

67° 

490,000 

+450,000 

W  190,000 

1825 

121° 

69° 

287° 

282° 

102° 

420,000 

+405,000 

E  90.000 

1826 

151° 

81° 

292° 

284° 

139° 

390,000 

+255,000 

E  290,000 

1827 

181° 

93° 

296° 

286° 

176° 

400,000 

+  30,000 

E  400,000 

1828 

212° 

105° 

300° 

288° 

208° 

425,000 

—205,000 

E  370,000 

1829 

242° 

117° 

304° 

291° 

240° 

450,000 

—385,000 

E  225,000 

1830 

272° 

130° 

309° 

293° 

264° 

470,000 

470,000 

E  45,000 

1831 

303° 

142° 

313° 

295° 

291° 

460,000 

—425,000 

W  160,000 

1832 

333° 

154° 

317° 

297° 

318° 

420,000 

—280,000 

W  320,000 

1833 

3° 

166° 

322° 

299° 

346° 

360,000 

—  90,000 

W  350,000 

1834 

34° 

178° 

326° 

302° 

18° 

290,000 

+  90,000 

W  275,000 

1835 

64° 

191° 

330° 

304° 

65° 

225,000 

+200,000 

W  100,000 

1836 

94° 

203° 

334° 

306° 

116° 

230,000 

+200,000 

E  100,000 

1H37 

125° 

215° 

339° 

308° 

167° 

290,000 

+  60,000 

E  285,000 

51 


Table 

II  (Coi 

tinned). 

Position  of  planets  in 
gitude  on  January  Is 

heliocentric  lon- 
,t  of  each  year 

Direction   and    dis- 
tance   from    sun    to 
center  of  gravity  of 
system 

Sun's  position  relative  to  its 

apex  and  to  center  of 

gravity 

Year 

Jup. 

Sat. 

Ura. 

Nep. 

Direction 
in  heliocen-  Distance 
trie  long,      in  miles 

On  the 
course, 
miles 

Off  the 
course, 
miles 

1838 

155° 

227° 

343° 

310° 

197° 

440,000 

—120,000 

E  420,000 

1839 

185° 

240° 

347° 

312° 

224° 

560,000 

—390,000 

E  400,000 

1840 

216° 

252° 

352° 

315° 

247° 

680,000 

620,000 

E  270,000 

1841 

246° 

264° 

356° 

317° 

268° 

770,000 

—775,000 

E     30,000 

1842 

272° 

276° 

354° 

319° 

288° 

845,000 

—805,000 

W  270,000 

1843 

303° 

287° 

357° 

321° 

307.5° 

880,000 

—705,000 

W  535,000 

1844 

335° 

298° 

1° 

323° 

327.5° 

880,000 

—465,000 

W  750,000 

1845 

8° 

309° 

5° 

326° 

347.5° 

840,000 

—175,000 

W  825,000 

1846 

42° 

320° 

9° 

328° 

7° 

775,000 

+  95,000 

W  770,000 

1847 

74° 

332° 

13° 

330° 

25° 

680,000 

+285,000 

W  610,000 

1848 

105° 

343° 

17° 

332° 

45° 

525,000 

+375,000 

W  370,000 

1849 

135° 

355° 

21° 

334° 

65° 

390,000 

+350,000 

W  170,000 

1850 

163° 

8° 

25° 

336° 

86° 

220,000 

+215,000 

W    15,000 

1851 

191° 

20° 

29° 

339° 

134° 

50,000 

+  35,000 

E     40,000 

1852 

218° 

33° 

33° 

341° 

285° 

120,000 

—120,000 

W    30,000 

1853 

247° 

46° 

37° 

343° 

312° 

285,000 

—215,000 

W  190,000 

1854 

277° 

62° 

41° 

345° 

334° 

440,000 

—200,000 

W  390,000 

1855 

308° 

74° 

45° 

347° 

353° 

565,000 

—  65,000 

W  560,000 

1856 

340° 

88° 

50° 

350° 

13° 

640,000 

+  145,000 

W  625,000 

1857 

13° 

101° 

54° 

352° 

34° 

710,000 

+400,000 

W  595,000 

1858 

46° 

114° 

58° 

354° 

55° 

735,000 

+600,000 

W  430,000 

1859 

78° 

128° 

62° 

356° 

76° 

730,000 

+710,000 

W  170,000 

1860 

109° 

142° 

66° 

357° 

100° 

710,000 

+700,000 

E  120,000 

1861 

139° 

154° 

71° 

359° 

124° 

660,000 

+545,000 

E  370,000 

1862 

167° 

167° 

75° 

1° 

150° 

610,000 

+305.000 

E  530,000 

1863 

194° 

179° 

79° 

4° 

179° 

555,000 

+  10,000 

E  555,000 

1864 

222° 

192° 

83° 

5° 

208° 

510,000 

—250,000 

E  450,000 

1865 

251° 

204° 

88° 

7° 

238.5° 

480,000 

—410,000 

E  245,000 

1866 

280° 

215° 

92° 

10° 

270° 

460,000 

—460,000 

W    10,000 

1867 

311° 

226° 

96° 

12° 

302.5° 

460,000 

—390,000 

W  245,000 

1868 

341° 

238° 

101° 

14° 

334° 

445,000 

—200,000 

W  400,000 

1869 

18° 

249° 

105° 

16° 

2° 

445,000 

+  10,000 

W  445,000 

1870 

51° 

260° 

110° 

19° 

29° 

410,000 

+200,000 

W  360,000 

1871 

82° 

271° 

114° 

21° 

66° 

355,000 

+295.000 

W  200,000 

1872 

113° 

282° 

119° 

23° 

90° 

315,000 

+305,000 

0    000,000 

1873 

143° 

293° 

124° 

25° 

128° 

365,000 

+205,000 

E  160,000 

1874 

171° 

304° 

128° 

28° 

176° 

230,000 

+  15,000 

E  230,000 

52 


Table  II  (Continued). 


Position  of  planets  In  heliocentric  lon- 
gitude on  January  1st  of  each  year 

Direction  and  dis- 
tance from  sun  to 
center  of  gravity  of 
system 

Sun's  position  relative  to  its 

apex  and  to  center  of 

gravity 

Year 

J  up. 

Sat. 

Ura. 

Nep. 

Diiection 
in  heliocen-  Distance 
trie  lonK-   in  miles 

On  the 
course, 
miles 

Off  the 

course, 

miles 

1875 

199^^ 

316° 

133° 

30° 

222° 

250,000 

—165,000 

E  180,000 

1876 

226° 

327° 

137° 

32° 

265° 

335,000 

—335,000 

E  30,000 

1877 

255° 

339° 

142° 

34° 

298° 

435,000 

—390,000 

W  200,000 

1878 

284° 

350° 

142° 

36° 

323.5° 

550,000 

—330,000 

W  445,000 

1879 

316° 

3° 

152° 

38° 

347° 

645,000 

—150,000 

W  630,000 

1880 

348° 

15° 

156° 

41° 

10° 

730,000 

+120,000 

W  720,000 

1881 

22° 

28° 

161° 

43° 

32° 

785,000 

+405,000 

W  670,000 

1882 

55° 

41° 

166° 

45° 

53° 

810,000 

+640,000 

W  485,000 

1883 

87° 

54° 

170° 

48° 

74° 

810,000 

+775,000 

W  225,000 

1884 

118° 

68° 

175° 

50° 

95° 

775,000 

+770,000 

E  60,000 

1885 

147° 

81° 

180° 

52° 

116° 

715,000 

+655,000 

E  315,000 

1886 

175° 

95° 

185° 

54° 

138° 

630,000 

+425,000 

E  470,000 

1887 

203° 

109° 

189° 

57° 

160° 

530,000 

+175,000 

E  500,000 

1888 

230° 

122° 

194° 

59° 

187° 

395,000 

'  _  45,000 

E  390,000 

1889 

259° 

136° 

199° 

61° 

217° 

280,000 

—165,000 

E  225,000 

1890 

289° 

149° 

203° 

63° 

261° 

185,000 

—180,000 

E  35,000 

1891 

321° 

162° 

208° 

66° 

330° 

150,000 

—  75,000 

W  135,000 

1892 

354° 

174° 

213° 

68° 

25° 

225,000 

+  95,000 

W  200,000 

1893 

27° 

187° 

217° 

70° 

60° 

310,000 

+270,000 

AV  155,000 

1894 

60° 

199° 

222° 

72° 

88° 

405,000 

+405,000 

W  10,000 

1895 

92° 

210° 

226° 

75° 

115° 

480,000 

+435,000 

E  200,000 

1896 

122° 

222° 

231° 

77° 

140° 

540,000 

+340,000 

E  410,000 

1897 

151° 

233° 

235° 

79° 

166° 

590,000 

+140,000 

E  570,000 

1898 

179° 

245° 

240° 

81° 

190° 

620.000 

—110,000 

E  605,000 

1899 

207° 

256° 

244° 

84° 

217° 

630,000 

—380,000 

E  500,000 

1900 

235° 

267° 

249° 

86° 

243° 

640,000 

—570,000 

E  300,000 

1901 

263° 

278° 

253° 

88° 

268° 

645,000 

—645,000 

E  10,000 

1902 

294° 

288° 

257° 

90° 

296° 

645,000 

—585,000 

W  280,000 

1903 

326° 

300° 

262° 

92° 

320° 

640,000 

410,000 

W  500,000 

1904 

359° 

311° 

266° 

95° 

347° 

630,000 

—140,000 

W  620,000 

1905 

32° 

322° 

270° 

97° 

15° 

570,000 

+145,000 

W  555,000 

1906 

65° 

333° 

274° 

99° 

42° 

540,000 

+355,000 

W  400,000 

1907 

96° 

346° 

279° 

101° 

68° 

490,000 

1  +450,000 

W  180,000 

1908 

126° 

358° 

283° 

103° 

93° 

420.000 

1  +425.000 

E  25,000 

1909 

155° 

10° 

287° 

106° 

121° 

340,000 

1  +290,000 

E  180,000 

1910 

183° 

23° 

291° 

108° 

150° 

280,000 

1  +135,000 

E  235,000 

TABLE    III. 

OF  Path  of  Sun  During  Three  Great  Tear  Periods. 


X  Slenlfies  s 

un  cr 

sBine  path 

oI_ce 

nter  of  eravl 

y- 

Middle  ordl- 

Middle  ordl- 

MIddleordI 

Middle  ordl- 

Middle  ordi 

Middle  nrdl- 

West — miles 

X 

Year 
1486.35 

East— miles 

West — miles 

X 

1663.65 

C-. 

East— miles 

West— miles 

X 

1841.1 

X 

East-mlles 

540,000 

.n 

1489 

715,000 

1667 

-I' 

820,000 

1845 

3 

^ 

1493.24 

X 

^: 

1671.95 

X 

O 

1850.3 

X 

m 

1495 

•p 

120,000 

"^■ 

1673 

o 

400,000 

1851 

30,000 

X 

1496.2 

^ 

X 

1673.55 

=\ 

X 

18.51.6 

". 

690,000 

.o 

1500 

•^ 

690,000 

in 

1678 

c; 

620,000 

m 

1856 

'"■ 

1504.07 

X 

'^ 

1681.9 

X 

CO 

1859.6 

X 

" 

1507 

CO 

480,000 

'^ 

1685 

^J 

500,000 

" 

1863 

_^ 

560,000 

X 

1509.95 

'^■ 

X 

1687.9 

O) 

X 

1865.95 

« 

425,000 

s 

1513 

'-' 

450,000 

in 

1691 

'"' 

440,000 

1869 

d 

1516 
1518 

X 

230,000 

d 

1694.1 
1696 

X 

210,000 

d 

1S72 
1874 

X 

230,000 

X 

1520.15 

^ 

X 

1698.05 

ii 

X 

1876.15 

rt 

850,000 

in 

1524 

'" 

785,000 

f-t 

1702 

^ 

710.000 

i_- 

1880 

'^ 

o 

1528.75 
1531 

X 

260,000 

n 

1706.3 
1709 

X 

380,000 

-1* 

1883.8 
1887 

X 

500,000 

X 

1533.2 

d 

X 

1711.76 

m 

X 

1890.2 

d 

360,000 

- 

1536 
1538.55 

X 

260,000 

- 

1714 
1716.2 

X 

200.000 

» 

1892 
1894.05 

X 

*"• 

1542 

615,000 

^ 

1720 

630,000 

2 

1898 

600,000 

X 

1545.4 

t^ 

X 

1723.28 

= 

X 

1901.05 

^. 

560,000 

1549 

s 

570.000 

,^ 

1727 

-*> 

600,000 

1904 

2 

d 

1552.3 

X 

*. 

1730.02 

X 

1907.86 

X 

1554 

185,000 

'^ 

1732 

210.000 

1910 

230,000 

X 

1556 

d 

X 

1734.15 

d 

560,000 

X 

1560 
1562.8 
1566 
1569.95 

X 

055,000 

470,000 

X 

1738 
1740.5 
1744 
1747.8 

X 

CO 

690,000 

275,000 

in 

1572 

^ 

300.000 

n 

1750 

*"* 

o 
d 

1574.65 
1577 

X 

370,000 

o 
c 

1752.8 
1755 

X 
t- 

335,000 

X 

1580 

'-^ 

X 

1758.1 

^ 

720,000 

X 

1584 
1587.5 
1590 
1593.3 

X 

410,000 

650,000 

X 

1762 
1765.05 
1768 
1771.9 

X 

530,000 

210,000 

X 

1595 
1597.3 
1601 
1605.2 

X 

730,000 

110,000 

X 

1774 
1774.8 
1779 
1783.1 

X 

750,000 

445,000 

.n 

1608 

3 

430.000 

.n 

1786 

s 

o 

1610.8 
1613.5 

X 

350,000 

S 

1788.6 
1792 

X 

420,000 

X 

1616.25 

o 

X 

1794.65 

-1^ 

340,000 

o 

1619 
1621.3 

X 

290.000 

" 

1797 
1799.05 

X 

rt 

1625 

^ 

870,000 

s 

1S03 

■^ 

850,000 

X 

1630.35 

_; 

X 

1807.8 

ci 

70,000 

X 

1632 
1632.7 
1637 
1639.9 

X 

530,000 

200,000 

X 

1810 
1811.65 
1815 
1817,25 

X 

o 

375,000 

590,000 

t— 
X 

1643 
1646.45 
1649 
1652.65 

X 

460,000 

710,000 

X 

1821 
1824.7 

1827 
1830.2 

X 

400,000 

250,000 

o 

1655 

350,000 

m 

1833 

^ 

1657.05 

X 

^. 

1S35.5 

X 

'^ 

1660.5 

550.000 

^ 

1838 

420,000 

i 


m 


> 

LJ 

-I 
ffl 

< 
I- 


Table  of  Mercury's  Orbit 

Sun   advancing 

miles  per  sec- 

Sun's  speed 

at  IS   n-lles 

at  33  miles 

sun's  speed 

It  fill  t  miles. 

end.    5    days  = 

2.000  miles* 

of 

Ef 

Heliocentric 
longitude 

Vector 

Depart 

re               Departure 

Mercury's  latitude  south  of 
starling  point 

rlflamirde 

coursB 

Sun's 

Mercury's 

<5un'5 

Mercury's 

Sun's 

Mercur  's 

' 

Plus 

„,„„. 

latitude 

position 

laUluJe' 

position 

latitude 

position 

LamuTe' 

0 

0 

90°  00' 

28.500.000 

I.I 

0 

0 

28.500.000 

0 

28,500,000 

0 

28.500,000 

0 

28.500,000 

0 

1 

5 

120°  19' 

29,800,000 

15,100 

Olio 

2.700.000 

2,700,000 

30.660,000 

4,860,000 

35,400,000 

9,610,000 

42.750,000 

16.9.50,000 

58,500,000 

32,700.000 

2 

10 

147°  16' 

32,100,000 

27,0110 

null 

8,300,000 

11,000,000 

32,820,000 

15.320,000 

42,320,000 

24,820.000 

57.010.000 

39,510,000 

88,500,000 

71,400,000 

3 

15 

170°  19' 

33,800,000 

34,300 

mill 

11,500,000 

22,500,000 

34,980,000 

28,980,000 

49,240,000 

43,240,000 

71.270.000 

65.270.000 

118,500.000 

112.500,000 

i 

20 

190°  00' 

37,300,000 

36,8011 

mill 

12,600,000 

35,100,000 

37,140,000 

43,740.000 

56,140,000 

62,740,000 

85.520,000 

92,120,000 

148.500,000 

155.100.000 

5 

25 

207°  11' 

39,600,000 

35,200 

mill 

11,600,000 

46,700,000 

39,300,000 

57,500,000 

63,060,000 

81,260,000 

99.780.000 

117,980,000 

178,500,000 

196.700,000 

6 

30 

222°  40' 

41,350,000 

30,400 

Olio 

9,800,000 

56,500,000 

41,460,000 

69,460,000 

69,970,000 

97,970,000 

114.040.000 

142.040,000 

208,500.000 

236,500,000 

7 

35 

237°  05' 

42,550,000 

23.200 

lino 

7,900,000 

64,400.000 

43.620,000 

79,520,000 

76,880.000 

112.780,000 

128.290,000 

164.190.000 

238.500.000 

274,400,000 

8 

40 

250°  56' 

43,100.000 

14.2011 

Olio 

4,900,000 

69,300.000 

45,780,000 

86.580,000 

83,790,000 

124.590.000 

142,550,000 

183,350,000 

268,500,000 

309,300,000 

9 

45 

264°  41' 

43,100,000 

4,000 

IIOll 

2,100,000 

71,400,000 

47,940,000 

90,840,000 

90,710,000 

133.610.000 

156,800.000 

199,700,000 

298,500,000 

341.400,000 

47 

270°  15' 

42.900.000 

71,400.000 

50.100,000 

0 

93,470,000 

136.370.000 

0 

0 

316,500,000 

351,500,000 

10 

3 

278°  46' 

42.300.000 

6.500,000 

1.100.000 

70.300.000 

52,260,000 

94.060.000 

97,020.000 

139.420.000 

171.000.000 

212,286,000 

328,500.000 

370,300,000 

11 

8 

293°  37' 

41.000.000 

16.400.000 

4.300,000 

66,000,000 

54.420,000 

91.920,000 

104.530.000 

142,030.000 

185.000.000 

222,820,000 

358,500.000 

396.000,000 

12 

13 

309°  46' 

39.100.000 

25,000,000 

7,400,000 

58,600,000 

56,580,000 

86,680,000 

111.440,000 

141,540.000 

199,570.000 

229,670,000 

388.500,000 

418,600,000 

13 

18 

327°  51' 

36.700,000 

31,000,000 

1 

10,400,000 

48,200,000 

58,740,000 

78,440,000 

118,360,000 

138,060,000 

213.830.000 

233,530.000 

418.500.000 

438,200,000 

14 

23 

348°  35' 

33.900.000 

33,350,000 

12,900,000 

35,300,000 

60,900,000 

67,700,000 

125,270,000 

132,070.000 

228,080,000 

2.34,880,000 

448,500,000 

455,300,000 

15 

28 

12°  32' 

31,400,000 

30,600,000 

13,700,000 

21.600,000 

63,060,000 

56,160,000 

132,180,000 

125,280,000 

242,340,000 

235,440,000 

478,500,000 

471,600,000 

16 

33 

40°  20' 

29,300,000 

22.400.000 

12,100.000 

9,500,000 

65.220,000 

46,220,000 

139,100,000 

120,100,000 

256,600,000 

237,600,000 

508,500,000 

489.500,000 

17 

38 

71°  4' 

28,400,000 

9.200.000 

7,900.000 

1,600,000 

67.380,000 

40,480,000 

146,000,000 

119.100.000 

270,850,000 

243.950,000 

538.500,000 

511.600.000 

18 

41 

90°  00' 

28.500.000 

0 

1.600.000 

0 

68.650,000 

40.150.000 

150,100,000 

121.600.000 

279,290,000 

250,790.000 

556,260,000 

527.760.000 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

PERNAU    PUBLISHING  CO. 

423    HAYES    STREET 

SAN    FRANCISCO,   CAL. 


QC 
-^3 


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